# LCM: when calculating, is there a better method than...?

#### John Whitaker

##### Junior Member
When calculating the LCM of two numbers like 13 & 32, (ans. 416), is there a shortcut method of reaching this answer without creating two long lists of numbers like
13, 26, 39, 52... and 32, 64, 96, 128... all the way to 416? Thank you.

#### galactus

##### Super Moderator
Staff member
Re: LCM

Yes, there is. Use their factorizations.

$$\displaystyle 13=13$$

$$\displaystyle 32=2^{5}$$

Now, use the largest of each. Sinc there are only two, $$\displaystyle 13\cdot{2^{5}}=416$$

#### Loren

##### Senior Member
Re: LCM

Example:
Find the LCM of 6,8,12 and 18.

Factor each and express in exponential form.

6 = 2*3
8 = 2^3
12 = 2^2*3
18 = 2*3^2

To get the LCM select each base with its largest exponent and multiply them together.

LCM is (2^3)(3^2) = 8*9 = 72.

#### John Whitaker

##### Junior Member
Re: LCM

Thank you. Got it.