How to find LCM: Lowest Common Multiple | Class 5 - Orchids

# Factors and Multiples

## Least Common Multiple for Class 5 Math

The full form of LCM is the least common multiple. Here students will learn the LCM definition and LCM meaning.

In this learning concept, the students can

• Representation of the LCM by prime factorization method and LCM by division method.
• Interpret how to find the LCM of two numbers.
• Application of LCM question word problem.

Each concept is explained to class 5 maths students using illustrations, examples, and mind maps. Students can assess their learning by solving the two printable worksheets given at the pageâ€™s end.

Download the LCM question worksheet for class 5 and check the solutions for the concept of the LCM question provided in PDF format.

## What Is LCM?

• The multiples of the number are the number multiplied by the natural number.
• The common multiples of the number are the multiples that are common in two or more sets of multiples.

### Example:

• The first few multiples of the numbers 2 and 3 are
• Multiples of 2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, â€¦.

Multiple of 3 = 3, 6, 9, 12, 18, 21, 24, 27, â€¦â€¦

• The common multiples of 2 and 3 are the list of numbers common in the multiples of 2 and 3.
• Therefore, the common multiples of 2 and 3 are: 6, 12, 18, 24, and so on.

Least Common Multiples

• The least common multiple is the smallest of the common multiples.
• It is also written as LCM.

Methods to Find LCM

• Common multiples method
• Prime factorization method
• Division method

## How to Find the LCM of Two Numbers?

• Write the multiples of the numbers.
• List the common multiples of the numbers.
• Choose the smallest common multiple.

### Example:

Find the least common multiples of 2 and 3

Solution:

The multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, â€¦

The multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, â€¦.

The common multiples of 2 and 3 are 6, 12, 18, 24, 30, 36, â€¦

The smallest of the common multiple of 2 and 3 is 6. Therefore, LCM or the least common multiple of 2 and 3 is 6.

## LCM by Prime Factorization Method

• Write the prime factorization of each number.
• List each unique factor that appears the greatest number of times.
• Multiply the factors.

### Example:

Find the LCM of 12 and 16.

Solution:

Step 1:

Find the prime factorization of 12.

Step 2:

Find the prime factorization of 16.

Step 3:

12 = 2 Ã— 2 Ã— 3

16 = 2 Ã— 2 Ã— 2 Ã— 2

LCM = 2 Ã— 2 Ã— 2 Ã— 2 Ã— 3

= 48

## LCM by Division Method

• Write the given numbers in the first line.
• Divide the number by the smallest prime numbers.
• Write the dividend in the next line and rewrite the number if it is not divided.
• Repeat the process till you get a prime number with no common factors.
• Multiply the divisor of each step.

### Example:

Find the LCM of 8 and 16.

Solution:

LCM = 2 Ã— 2 Ã— 2 Ã— 2

= 8

## LCM Questions Word Problem:

### Example:

A candle seller sells candles in a packet of 12 and a candle stands in a packet of 8. What is the least number of candles and candle stand that he should sell so that there will be one candle for each stand?

Solution:

Number of candles in a packet = 12

Number of candle stands in a packet = 8

Obtain the least common multiple of 12 and 8.

12 = 2 Ã— 2 Ã— 3

8 = 2 Ã— 2 Ã— 2

LCM = 2 Ã— 2 Ã— 2 Ã— 3

= 24

Therefore, he should sell at least 24 candles.

Fun Facts:

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