### Math - Class 6 - Chapter 3 – Playing With Numbers (Least Common Multiple (LCM)/ Lowest Common Multiple) - Key Points/Notes/Worksheets/Explanation/Lesson

**Tags:**Least common multiple for class VI, Lowest common multiple for 6^{th}class, Find the Least Common Multiple for sixth standard, least common multiple examples for grade VI, Free Worksheets PDF and Practice Page on LCM, How to find least common multiple? What is LCM? How do you find the least common multiple? LCM by Prime Factorization Method, LCM by Division Method, LCM of 12 and 15. Find LCM of 16, 24 and 56. Find LCM of 20, 25 and 30. Find LCM of 28 and 126. Find the LCM of 25 and 85 by prime factorization method. What is the least common multiple that is a multiple of 48, 72 and 108?### Lowest Common Multiple (LCM)

**Lowest Common Multiple**The Lowest Common Multiple (LCM) of two or more given number is the lowest (or smallest or least) of their common multiples.

Example: LCM of 12 and 15.

Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252…

Multiples of 15 are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240…

Common Multiples of 12 and 15 are 60, 120, 180, 240…

Lowest Common Multiples of 12 and 15 is

**60**. (60 is the smallest number that both the numbers are factors of this number.)**LCM by Prime Factorization Method**__Example:__Find LCM of 16, 24 and 56**Step1:**Find out the prime factors of the given numbers.2

16

2

8

2

4

2

2

1

2

24

2

12

2

6

3

3

1

2

56

2

28

2

14

7

7

1

Prime factor of 16 = 2 x 2 x 2 x 2 = 2

^{4 }Prime factor of 24 = 2 x 2 x 2 x 3 = 2

^{3 }x 3Prime factor of 56 = 2 x 2 x 2 x 7 = 2

^{3 }x 7**Step2:**Identify the maximum number of occurrence of each prime number. Here, 2^{4 }(2 has occurred 4 times), 3^{1}(3 has occurred 1 time) and 7^{1}(7 has occurred 1 time)**Step3:**Now multiply the outcomes.2 x 2 x 2 x 2 x 3 x 7 = 336

**LCM by Division Method****Step 1:**Find the prime factors of the two or more numbers by dividing the numbers by least prime number till we get 1. (Choose the least prime that at least divide one of the given numbers)**Step 2:**Then multiply all the prime factors to get the LCM.__Example:__Find LCM of 20, 25 and 302

20, 25, 30

2

10, 25, 15

3

5, 25, 15

5

5, 25, 5

5

1, 5, 1

1, 1, 1

LCM of 20, 25 and 30 = 2 x 2 x 3 x 5 x 5 = 300

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