# What is the least common multiple of 32, 15, and 36?

May 10, 2016

$\text{LCM} \left(32 , 15 , 36\right) = 1440$

#### Explanation:

To find the least common multiple, we can look at the prime factorization of all of our given values, and then take the power of the highest power used of each prime. By doing so, we ensure that the prime factorization of our LCM contains the prime factorizations of all initial values, meaning it is divisible by each.

$32 = {2}^{5}$
$15 = 3 \cdot 5$
$36 = {2}^{2} \cdot {3}^{2}$

The highest power of $2$ used is $5$.
The highest power of $3$ used is $2$.
The highest power of $5$ used is $1$.
No other primes were used.

By the above, then, the LCM will be

${2}^{5} \cdot {3}^{2} \cdot 5 = 1440$