# How do you find the LCM of 15, 20?

Nov 28, 2016

## 60

#### Explanation:

method 1

write out the multiples of both numbers until the lowest common one id found

multiples 15:$\text{ } \left\{15 , 30 , 45 , \textcolor{b l u e}{60} , 75 , 90 , 105 , \textcolor{b l u e}{120} , 135 , \ldots\right\}$

multiples 20:$\text{ } \left\{20 , 40 , \textcolor{b l u e}{60} , 80 , 100 , \textcolor{b l u e}{120} , \ldots\right\}$

$L C M \left(15 , 20\right) = 60$

method 2

use $h c f \times \lcm = a \times b$

$h c f = g c m \left(15 , 20\right) = 5$

so$\text{ } 5 \times \lcm = 15 \times 20$

$\lcm = \frac{15 \times 20}{5}$

cancel before evaluating makes it easier.

$\lcm = \frac{{\cancel{15}}^{3} \times 20}{\cancel{5}} = 60$
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