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
- 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.
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€¦
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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