# Thread: what is the common multiple ..

1. ## what is the common multiple ..

of 20 and 36

2. Originally Posted by ckica
of 20 and 36
Hi ckica,

I guess you're looking for the least common multiple, right?

Factor each value using prime factors:

$20=2^2 \cdot 5$

$36=2^2 \cdot 3^2$

Now multiply all the different factors using their greatest exponent:

$LCM=2^2 \cdot 3^2 \cdot 5=180$

3. Oh thanks you so much so the answer is 180?

4. Originally Posted by ckica
Oh thanks you so much so the answer is 180?
It is if you're looking for the least common multiple, which I assumed.

List the multiples of 20 and 80. You see that 180 is the first multiple common to both. There is an infinite numbers of common multiples, but 180 is the least common multiple (LCM).

20, 40, 60, 80, 100, 120, 140, 160, 180

36, 72, 108, 144, 180