LCM for Class 5 Step by Step with Easy Examples

The Least Common Multiple (LCM) is an important maths concept that helps Class 5 students solve problems easily. In this article, students will learn that the Least Common Multiple (LCM) is the smallest number that is a common multiple of two or more numbers.

Table of Contents

• What is LCM?
• Formula for LCM
• Methods to Find LCM
• Solved Examples on LCM for Class 5
• Practice Questions on LCM for Class 5
• LCM Worksheet for Class 5

What is LCM?

LCM stands for Least Common Multiple. It is also called the Lowest Common Multiple. The LCM of two or more numbers is the smallest number that is a multiple of all of them.

The least common multiple is the smallest of all the common multiples. In the example above, the common multiples of 4 and 6 are 12, 24, 36, and so on. The least common multiple is 12. This is the smallest number that is a multiple of both 4 and 6.

We can write this as LCM of 4 and 6 is 12, or we can write it as LCM (4, 6) = 12.

Formula for LCM

There is no single formula to directly calculate LCM like we have in basic arithmetic. However, we can use different methods to find the LCM of two or more numbers systematically.

The relationship between LCM and HCF is given by the formula:

Where:

• a and b are any two numbers
• LCM is the Least Common Multiple
• HCF is the Highest Common Factor

We can rearrange this formula to find LCM if we know HCF:

EXAMPLE :

Let us find the LCM of 12 and 18 using the HCF.

• LCM (12, 18) = 36
• HCF (12, 18) = 6
• LCM × HCF = 36 × 6 = 216
• Product = 12 × 18 = 216
• The formula is verified: 216 = 216

Methods To Find LCM

There are different methods to find the LCM of two or more numbers. Let us learn each method in detail.

Method 1: Listing Multiples Method

This is the simplest method to find LCM. In this method, we list the multiples of each number until we find a common multiple. The smallest common multiple is the LCM.

Step 1: List the first several multiples of the first number.

Step 2: List the first several multiples of the second number.

Step 3: Look for multiples that appear in both lists.

Step 4: Find the smallest common multiple. This is the LCM.

EXAMPLE 1:

Find the LCM of 3 and 5.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

Common multiples: 15, 30, 45

Least common multiple: 15

Therefore, LCM (3, 5) = 15

EXAMPLE 2:

Find the LCM of 4 and 6.

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54

Common multiples: 12, 24, 36

Least common multiple: 12

Therefore, LCM (4, 6) = 12

Method 2: Prime Factorization Method

In this method, we find the prime factors of each number. Then we multiply the highest powers of all prime factors to get the LCM.

Step 1: Find the prime factorization of the first number.

Step 2: Find the prime factorization of the second number.

Step 3: Identify all prime factors that appear in either number.

Step 4: For each prime factor, take the highest power that appears.

Step 5: Multiply all these factors together. This is the LCM.

We take the highest power of each prime factor, not the lowest.

EXAMPLE 1:

Find LCM of 12 and 18.

Prime factorization of 12: 2 × 2 × 3 = 2² × 3

Prime factorization of 18: 2 × 3 × 3 = 2 × 3²

All prime factors: 2 and 3

Highest powers: 2² and 3²

LCM = 2² × 3² = 4 × 9 = 36

Therefore, LCM (12, 18) = 36

Method 3: Common Division Method

In this method, we divide the numbers by common factors and continue until we cannot divide anymore. Then we multiply all the divisors and the remaining numbers.

Step 1: Write the two numbers in a row.

Step 2: Find a number that divides both numbers.

Step 3: Divide both numbers by this number and write the quotients below.

Step 4: Repeat this process until no more common factors exist.

Step 5: Multiply all the divisors and the remaining numbers. This is the LCM.

EXAMPLE:

Find LCM of 12 and 18.

2 | 12    18
3 |  6     9
  |  2     3

LCM = 2 × 3 × 2 × 3 = 36

Now 2 and 3 have no common factor other than 1.

LCM = 2 × 3 × 2 × 3 = 36

Therefore, LCM (12, 18) = 36

Method 4: Using HCF Formula

In this method, we first find the HCF of the two numbers. Then we use the formula HCF × LCM = Product of the two numbers to find the LCM.

Step 1: Find the HCF of the two numbers using any method.

Step 2: Use the formula: LCM = (Product of the two numbers) ÷ HCF

Step 3: Calculate the LCM.

EXAMPLE:

Find LCM of 12 and 18.

First, find HCF (12, 18).

HCF (12, 18) = 6

Using the formula:

LCM = (12 × 18) ÷ 6

LCM = 216 ÷ 6

LCM = 36

Therefore, LCM (12, 18) = 36

Solved Examples on LCM for Class 5

QUESTION 1: FINDING LCM USING LISTING MULTIPLES METHOD

Problem: Find the LCM of 4 and 6.

Solution:

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48

Common multiples: 12, 24, 36

The least common multiple is 12.

Answer: LCM (4, 6) = 12

QUESTION 2: FINDING LCM USING PRIME FACTORIZATION

Problem: Find the LCM of 8 and 12.

Solution:

Prime factorization of 8: 2 × 2 × 2 = 2³

Prime factorization of 12: 2 × 2 × 3 = 2² × 3

All prime factors: 2 and 3

Highest powers: 2³ and 3¹

LCM = 2³ × 3 = 8 × 3 = 24

Answer: LCM (8, 12) = 24

QUESTION 3: FINDING LCM USING COMMON DIVISION METHOD

Problem: Find the LCM of 15 and 20.

Solution:

Prime factorization of 4: 2²

Prime factorization of 6: 2 × 3

Prime factorization of 8: 2³

All prime factors: 2 and 3

Taking highest powers: 2³ and 3¹

LCM = 2³ × 3 = 8 × 3 = 24

Answer: LCM (15, 20) = 60

QUESTION 4: FINDING LCM OF THREE NUMBERS

Problem: Find the LCM of 4, 6, and 8.

Solution:

Prime factorization of 4: 2²

Prime factorization of 6: 2 × 3

Prime factorization of 8: 2³

All prime factors: 2 and 3

Highest powers: 2³ and 3¹

LCM = 2³ × 3 = 8 × 3 = 24

Answer: LCM (4, 6, 8) = 24

QUESTION 5: WORD PROBLEM ON LCM

Problem: Ram goes to the library every 3 days. Shyam goes to the library every 5 days. If they both went to the library today, after how many days will they go together again?

Solution:

To find when they will go together again, we need to find the LCM of 3 and 5.

Multiples of 3: 3, 6, 9, 12, 15, 18, 21

Multiples of 5: 5, 10, 15, 20, 25, 30

Common multiples: 15, 30

The least common multiple is 15.

Answer: They will go to the library together after 15 days.

QUESTION 6: FINDING LCM WITH LARGER NUMBERS

Problem: Find the LCM of 24 and 36.

Solution:

Prime factorization of 24: 2³ × 3

Prime factorization of 36: 2² × 3²

All prime factors: 2 and 3

Highest powers: 2³ and 3²

LCM = 2³ × 3² = 8 × 9 = 72

Answer: LCM (24, 36) = 72

QUESTION 7: WORD PROBLEM ON TIMING

Problem: Bus A arrives at a stop every 6 minutes. Bus B arrives at the same stop every 8 minutes. If both buses just arrived, after how many minutes will they arrive at the same time again?

Solution:

To find when both buses will arrive together, we need to find the LCM of 6 and 8.

Prime factorization of 6: 2 × 3

Prime factorization of 8: 2³

All prime factors: 2 and 3

Highest powers: 2³ and 3¹

LCM = 2³ × 3 = 8 × 3 = 24

Answer: Both buses will arrive together after 24 minutes.

QUESTION 8: FINDING LCM USING HCF FORMULA

Problem: Find the LCM of 10 and 15 using the HCF formula.

Solution:

First, find HCF (10, 15).

Factors of 10: 1, 2, 5, 10

Factors of 15: 1, 3, 5, 15

HCF (10, 15) = 5

Using the formula: LCM = (Product of numbers) ÷ HCF

LCM = (10 × 15) ÷ 5

LCM = 150 ÷ 5

LCM = 30

Answer: LCM (10, 15) = 30

QUESTION 9: WORD PROBLEM ON REPEATING PATTERN

Problem: Anya eats an apple every 4 days. Bina eats an apple every 6 days. If they both ate an apple today, after how many days will they eat an apple on the same day again?

Solution:

To find when they will eat an apple on the same day, we need to find the LCM of 4 and 6.

Multiples of 4: 4, 8, 12, 16, 20, 24

Multiples of 6: 6, 12, 18, 24, 30

Common multiples: 12, 24

The least common multiple is 12.

Answer: They will eat an apple on the same day after 12 days.

QUESTION 10: FINDING LCM AND VERIFYING WITH FORMULA

Problem: Find the LCM of 8 and 12. Also verify using the HCF formula.

Solution:

Prime factorization of 8: 2³

Prime factorization of 12: 2² × 3

All prime factors: 2 and 3

Highest powers: 2³ and 3¹

LCM = 2³ × 3 = 8 × 3 = 24

To verify using the formula: HCF × LCM = Product of numbers

HCF (8, 12):

Factors of 8: 1, 2, 4, 8

Factors of 12: 1, 2, 3, 4, 6, 12

HCF (8, 12) = 4

Verification:

HCF × LCM = 4 × 24 = 96

Product of numbers = 8 × 12 = 96

The formula is verified: 96 = 96

Answer: LCM (8, 12) = 24, and the formula HCF × LCM = Product is verified.

Practice Questions on LCM for Class 5

QUESTION 1: BASIC LCM - LISTING MULTIPLES

Find the LCM of 2 and 3.

Solution:

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18

Multiples of 3: 3, 6, 9, 12, 15, 18, 21

Common multiples: 6, 12, 18

LCM (2, 3) = 6

Answer: 6

QUESTION 2: LCM OF TWO NUMBERS

Find the LCM of 5 and 7.

Solution:

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40

Multiples of 7: 7, 14, 21, 28, 35, 42, 49

Common multiples: 35

LCM (5, 7) = 35

Answer: 35

QUESTION 3: LCM USING PRIME FACTORIZATION

Find the LCM of 16 and 20.

Solution:

Prime factorization of 16: 2⁴

Prime factorization of 20: 2² × 5

All prime factors: 2 and 5

Highest powers: 2⁴ and 5¹

LCM = 2⁴ × 5 = 16 × 5 = 80

Answer: 80

QUESTION 4: LCM USING COMMON DIVISION

Find the LCM of 9 and 12.

Solution:

9 12

| |

÷ 3 3 4

Now 3 and 4 have no common factor.

LCM = 3 × 3 × 4 = 36

Answer: 36

QUESTION 5: LCM OF THREE NUMBERS

Find the LCM of 3, 4, and 5.

Solution:

Prime factorization of 3: 3

Prime factorization of 4: 2²

Prime factorization of 5: 5

All prime factors: 2, 3, and 5

Highest powers: 2², 3, and 5

LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60

Answer: 60

QUESTION 6: WORD PROBLEM - MEETING AGAIN

Rahul visits the park every 4 days. Neha visits the park every 6 days. If they both visited the park today, after how many days will they meet at the park again?

Solution:

We need to find the LCM of 4 and 6.

Multiples of 4: 4, 8, 12, 16, 20, 24

Multiples of 6: 6, 12, 18, 24, 30

Common multiples: 12, 24

LCM (4, 6) = 12

Answer: Rahul and Neha will meet at the park after 12 days.

QUESTION 7: LCM WITH SMALLER AND LARGER NUMBERS

Find the LCM of 6 and 9.

Solution:

Prime factorization of 6: 2 × 3

Prime factorization of 9: 3²

All prime factors: 2 and 3

Highest powers: 2 and 3²

LCM = 2 × 3² = 2 × 9 = 18

Answer: 18

QUESTION 8: WORD PROBLEM - ALARM BELLS

A bell rings every 8 minutes. Another bell rings every 12 minutes. If both bells ring together now, after how many minutes will they ring together again?

Solution:

We need to find the LCM of 8 and 12.

Prime factorization of 8: 2³

Prime factorization of 12: 2² × 3

All prime factors: 2 and 3

Highest powers: 2³ and 3

LCM = 2³ × 3 = 8 × 3 = 24

Answer: Both bells will ring together after 24 minutes.

QUESTION 9: LCM WITH COPRIME NUMBERS

Find the LCM of 7 and 9.

Solution:

7 and 9 are coprime numbers (they have no common factor other than 1).

For coprime numbers, LCM is equal to the product.

LCM (7, 9) = 7 × 9 = 63

Answer: 63

QUESTION 10: LCM OF EQUAL NUMBERS

Find the LCM of 5 and 5.

Solution:

Both numbers are the same.

LCM of a number with itself is the number itself.

LCM (5, 5) = 5

Answer: 5