# What is the LCM of 30 33?

330

#### Explanation:

Let's do the prime factorizations of both numbers first:

$30 = 2 \times 15 = 2 \times 3 \times 5$
$33 = \textcolor{w h i t e}{000000000000} 3 \times 11$

The LCM will have in it a $2 , 3 , 5$ from the $30$ and an $11$ from $33$ (there already being a $3$ from the $30$, so we get:

$2 \times 3 \times 5 \times 11 = 330$

$30 \times 11 = 330$
$33 \times 10 = 330$

Nov 15, 2016

Just another way.

Sometimes you can spot them and sometimes you can't. If you cant then it is a case of 'slogging' your way through to an answer.

$\textcolor{b l u e}{L C M = 330}$

#### Explanation:

$\textcolor{b l u e}{\text{Point 1}}$

Multiply 30 by any whole number and the last digit will be 0

Examples:
$30 \times 2 = 60$
$30 \times 21 = 630$

$\textcolor{b l u e}{\text{Point 2}}$

For the multiple to be common this means the last digit of
$33 \times$ something must also end in 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So we could test the first multiple of 33 in which the last digit is 0.

We know that $3 \times 10 = 30$
We also know that 3 multiplied by any number between 1 and 9 does not give 0 as a last digit. So 10 is a good candidate.

$\textcolor{red}{10 \times 33 = 330}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
All we need to do now is make sure that 30 divides exactly into 330
$3 \times 11 = 33$

multiply both sides by 10

color(red)("30xx11=330)