L.C.M Anyone?

I was teaching fractions to a student the other day. I then got onto the topic of adding fractions, I mentioned the word LCM. The student looked at me as though I was speaking a foreign language. I then tried to elaborate saying the words "Lowest Common Multiple", the student was still bemused. So I had to explain the concept to them. So this posting is for anybody who is confused with lowest common multiples.


Lowest Common Multiple

The smallest common multiple of two or more numbers is called the lowest common multiple (LCM).
E.g. Multiples of 8 are 8, 16, 24, 32, … Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, …

In general:

To find the lowest common multiple (LCM) of two or more numbers, list the multiples of the larger number and stop when you find a multiple of the other number. This is the LCM.

Example 3

Find the lowest common multiple of 6 and 9.

Solution:
List the multiples of 9 and stop when you find a multiple of 6.
Multiples of 9 are 9, 18, …Multiples of 6 are 6, 12, 18, …

Example 4

Find the lowest common multiple of 5, 6 and 8.
Solution:

List the multiples of 8 and stop when you find a multiple of both 5 and 6.
Multiples of 8 are 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, …
Stop at 120 as it is a multiple of both 5 and 6.
So, the LCM of 5, 6 and 8 is 120.