### Least Common Multiple (LCM)

**Tags**- Least Common Multiples, Multiples, Common Multiples, Examples of LCM, LCM worksheet PDF, Quiz on LCM, LCM Practice Page, LCM by prime factorization Method, LCM by division method. Find the least number that divides 10, 16 and 18Least Common Multiple (LCM)

**Multiples**Product of two given numbers is called

__multiples__. Multiple is the result of multiplying any number with other numbers like 1, 2, 3, 4 etc.__Example:__Multiple of 2 - 2, 4, 6, 8, 10, 12 and so on

Multiple of 3 – 3, 6, 9, 12, 15, 18, 21, and so on

**Common Multiples**Common multiple means a number that is multiple of two or more numbers.

__Example:__Multiple of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ….

Multiple of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 …..

Common multiple of 2 and 3 are 6, 12, 18 …..

**Least Common Multiples**The least common multiple (LCM) of two or more given number is the smallest number that is a multiple of all the given numbers.

__Example:__Find LCM of 12 and 18Multiples of 12 are 12, 24, 36, 48, 60, 72, 84…

Multiples of 18 are 18, 36, 54, 72, 90, 108…..

Common Multiples of 12 and 18 are 36, 72…

Least Common Multiples of 12 and 18 is 36, 72

**LCM by Prime Factorization Method**__Example:__Find LCM of 36 and 64**Step1:**Find out the prime factors of the given numbers.

Prime factor of 36 = 2 x 2 x 3 x 3 = 2

^{2 }x 3^{2}Prime factor of 64 = 2 x 2 x 2 x 2 x 2 x 2 = 2

^{6}**Step2:**Identify the maximum number of occurrence of each prime number.Here, 2

^{6 }(2 has occurred 6 times) and 3^{2}(3 has occurred 2 times)**Step3:**Now multiply the outcomes.2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 = 576

**LCM by Division Method**Find the prime factors of the two or more numbers by dividing the numbers till we get 1 and then multiply all the prime factors to get the LCM.

__Example:__Find LCM of 4, 6 and 82

4, 6, 8

2

2, 3, 4

2

2, 3, 2

3

1, 3, 1

1, 1, 1

LCM of 4, 6 and 8 = 2 x 2 x 2 x 3 = 24

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