# LCM

## 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 page’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, ….

Multiple of 3 = 3, 6, 9, 12, 18, 21, 24, 27, ……

• 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, …

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

The common multiples of 2 and 3 are 6, 12, 18, 24, 30, 36, …

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 × 2 × 3

16 = 2 × 2 × 2 × 2

LCM = 2 × 2 × 2 × 2 × 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 × 2 × 2 × 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 × 2 × 3

8 = 2 × 2 × 2

LCM = 2 × 2 × 2 × 3

= 24

Therefore, he should sell at least 24 candles.

Fun Facts:

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