What is the LCM of 30 33?

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What is the LCM of 30 33?

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Answer 1 · 2016-11-14T00:53:19

330

Explanation:

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

$30 = 2 \times 15 = 2 \times 3 \times 5$ $30=2xx15=2xx3xx5$
$33 = 0000000000003 \times 11$ $33=color(white)(000000000000)3xx11$

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

$2 \times 3 \times 5 \times 11 = 330$ $2xx3xx5xx11=330$

$30 \times 11 = 330$ $30xx11=330$
$33 \times 10 = 330$ $33xx10=330$

Answer 2 · 2016-11-15T21:57:38

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.

$L C M = 330$ $color(blue)(LCM = 330)$

Explanation:

$Point 1$ $color(blue)("Point 1")$

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

Examples:
$30 \times 2 = 60$ $30xx2 = 60$
$30 \times 21 = 630$ $30xx21 = 630$

$Point 2$ $color(blue)("Point 2")$

For the multiple to be common this means the last digit of
$33 \times$ $33xx$ 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 $3 \times 10 = 30$ $3xx10=30$
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.

$10 \times 33 = 330$ $color(red)(10xx33=330)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
All we need to do now is make sure that 30 divides exactly into 330
$3 \times 11 = 33$ $3xx11=33$

multiply both sides by 10

$30 \times 11 = 330$ $color(red)("30xx11=330)$

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What is the LCM of 30 33?

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