1Cademy - Finding the LCM of 24 and 36 Using Prime Factors

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Finding the LCM Using the Prime Factors Method

Example

Finding the LCM of 24 and 36 Using Prime Factors

To find the LCM of $24$ and $36$ , begin by writing each number as a product of primes: $24 = 2 \cdot 2 \cdot 2 \cdot 3$ and $36 = 2 \cdot 2 \cdot 3 \cdot 3$ . Align matching primes in columns:

$24 =$	$2$	$2$	$2$	$3$
$36 =$	$2$	$2$		$3$	$3$

Bring down one factor from each column: $2, 2, 2, 3, 3$ . Multiply: $\text{LCM} = 2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 = 72$ . Thus the LCM of $24$ and $36$ is $72$ .