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# What is the LCM of 18 and 24?

Sep 28, 2016

Least Common Multiple is $72$.

#### Explanation:

Multiples of $18$ are $\left\{18 , 36 , 54 , \textcolor{red}{72} , 90 , 108 , 126 , \textcolor{red}{144} , 162 , \ldots\right\}$

Multiples of $24$ are $\left\{24 , 48 , \textcolor{red}{72} , 96 , 120 , \textcolor{red}{144} , 168 , \ldots\right\}$

Hence, common multiples are $\left\{72 , 144 , \ldots \ldots \ldots . .\right\}$

and Least Common Multiple is $72$.

Jun 11, 2018

$L C M = 72$

#### Explanation:

Write each number as the product of its prime factors:

The LCM must contain all the factors of each number, but without any duplicates.

$\text{ } 18 = 2 \textcolor{w h i t e}{\times \times . x} \times 3 \times 3$
$\text{ } 24 = \underline{2 \times 2 \times 2 \times 3}$
$L C M = 2 \times 2 \times 2 \times 3 \times 3 = 72$