## How to Find the Least Common Multiple

written by: Suvo โข edited by: Trent Lorcher โข updated: 6/6/2012

In my childhood days, I was always afraid of Least Common Multiple and Greatest Common Factor. Well, now I am a math tutor and I have developed a simple method of explaining LCM. Don't be afraid of math like I was!

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If any number is multiplied by another number then the resulting number is called a multiple of the first number. For example, a multiple of 6 is 12. There may be many multiples of a number. For example, 12, 18, 24 are all multiples of 6.

If any number is divided by a number evenly (no remainder), then the second number is called a factor of the first number. For example, 6 is a factor of 12.

What is the Least Common Multiple?

This process will explain how to find the least common multiple (lcm) for a given set of numbers. In this example, we're using the numbers 12 and 15.

The multiples of 12 are 12x1, 12x2, 12x3, 12x4, 12x5, 12x6, 12x8, 12x9 and 12x10

=12, 24, 36, 48, 60, 72, 84, 96, 108,120

The multiples of 15 are 15, 30, 45, 60, 75, 90,105,120,135,150

Examine the list and find the common multiples from 12 and 15. You can see 60 and 120 show up in both lists.

So which is the least of the common multiples? That's easy: 60.

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### Another Way to Find LCM

Finding LCM for a set of numbers by the above method is bit cumbersome to do every time. Take the case of LCM of 7 and 84, by the above method we need to go on finding the multiples of 7 till 7x12.

Here's the short cut:

Start by factorizing both the number twelve and fifteen. Write down as below:

12=2 X 2 X 3=22 X 3

15=3 X 5

The prime factors from the result are 2, 3 and 5.

What are the highest degrees of these prime factors? In this case we have 22, 31, 51 by multiplying all these we have 4x3x5=60.

The LCM of the numbers is 60.