Hands-on math!

Least Common Multiple (LCM)

The least common multiple (LCM) of 2 numbers is the smallest number that they both divide evenly into. It is a bigger number than either of the 2 numbers.

One good way to find the least common multiple of 2 numbers is to multiply both numbers by 2,3,4,5... and then find the first multiple that appears in both lists.
For example, find the least common multiple of 6 and 8:

    Multiples of 6: 12 18 24 30 36 42 48 54 60 ...
    Multiples of 8: 16 24 32 40 48 56 64 72 80 ...

The first number that appears in both lists is 24. (48 appears also, but it is not 'least'), so 24 is the LCM of 6 and 8.

There is an equation for finding the LCM if you know the greatest common factor (GCF) of your 2 numbers.
Multiply the two numbers together and divide by their GCF:

The LCM of a and b:     LCM (a , b) = a x b / GCF (a , b)

For our example of 6 and 8 we have:

LCM (6 , 8) = 6 x 8 / GCF (6 , 8)     Since the greatest common factor of 6 and 8 is 2, we have:
LCM (6 , 8) = 6 x 8 / 2 = 48/2 = 24 <=== a shorter way!

Now, can you find the least common multiple of 10 and 35?