# What is the LCM of 31z^3, 93z^2?

Sep 24, 2015

$93 {z}^{3}$

#### Explanation:

LCM means the least number which is divisible by both $31 {z}^{3} \mathmr{and} 93 {z}^{2}$. It is obviuosly $93 {z}^{3}$, but it can be determined by factorisation method easily

$31 {z}^{3} = 31 \cdot z \cdot z \cdot z$
$91 {z}^{2} = 31 \cdot 3 \cdot z \cdot z$

First pick up the common factors 31zz and multiply the remaining numbers z*3 with this.

This makes up$31 \cdot z \cdot z \cdot 3 \cdot z = 93 {z}^{3}$

Sep 24, 2015

$93 {z}^{3}$

#### Explanation:

The LCM (Least Common Multiple) is the smallest value which each of two (or more) values divide evenly into.

Dividing $31 {z}^{2}$ and $93 {z}^{3}$ into factors and selecting all factors that are required by at least one of the two values:
{:(31z^3," = ", ,31, z, z, z), (93z^2," = ",3,31, z,z, ),("required factors:", ,3, 31, z, z, z) :}

The required factors of the LCM of $31 {z}^{3}$ and $93 {z}^{2}$ are
$3 \times 31 \times z \times z \times z$

$\Rightarrow L C M \left(31 {z}^{3} , 93 {z}^{2}\right) = 93 {z}^{3}$