What is the LCM of 30 33?

2 Answers
MathFact-orials.blogspot.com
Nov 14, 2016

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#

Tony B
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.

#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)#

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