Question

What is the LCM of 30 33?

Answer 1

330

Explanation:

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

`30=2xx15=2xx3xx5`
`33=color(white)(000000000000)3xx11`

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:

`2xx3xx5xx11=330`

`30xx11=330`
`33xx10=330`

Answer 2

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.

`color(blue)(LCM = 330)`

Explanation:

`color(blue)("Point 1")`

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

Examples:
`30xx2 = 60`
`30xx21 = 630`

`color(blue)("Point 2")`

For the multiple to be common this means the last digit of
`33xx` 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 `3xx10=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.

`color(red)(10xx33=330)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
All we need to do now is make sure that 30 divides exactly into 330
`3xx11=33`

multiply both sides by 10

`color(red)("30xx11=330)`