We can find a multiple by multiplying the numbers together, but to find the Least Common Multiple we have to get rid of any factors that the numbers have in common.

What’s the LCM of 4 and 6?

Multiples of 4: 4, 8, 12, 16, 20, 24 ….

Multiples of 6: 6, 12, 18, 24, 30, 36 …

How can we find the LCM without listing multiples? How can we “get rid of” the factor(s) that 4 and 6 have in common?

Use Prime Factors

Prime factors of 4: 2 X 2Prime factors of 6: 2 X 3

What do they have in common?

Now multiply what you have left2 X 2 X 3 = 12

Get rid of the second one.

Here’s how this works:Find the Least Common Multiple of 18 and 27.

Find primefactors.

18 27

2 92 3 3

3 9333

18 = 2 X 3 X 327 = 3 X 3 X 3

Find common factors.Get rid of the extras of each

repeated factor.Multiply what’s left -

2 X 3 X 3 X 3 = 54

54 is the Least Common Multiple

of 18 and 27.