# How do you find the GCF and LCM of numbers?

Apr 1, 2016

See explanation...

#### Explanation:

Given two numbers, you can find the GCF as follows:

Divide the larger number by the smaller to give a quotient and remainder.

If the remainder is zero, then the GCF is the smaller number.

Otherwise repeat with the smaller number and the remainder.

For example, to find the GCF of $252$ and $70$ proceed as follows:

$\frac{252}{70} = 3$ with remainder $42$

$\frac{70}{42} = 1$ with remainder $28$

$\frac{42}{28} = 1$ with remainder $14$

$\frac{28}{14} = 2$ with remainder $0$

So the GCF is $14$

Then to find the LCM, multiply the two original numbers together and divide by the GCF.

In our example, the LCM of $252$ and $70$ is:

$\frac{252 \cdot 70}{14} = 1260$