How do you use prime factorization to find the least common multiple of 75 and 45?

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Answer 1 · 2016-12-14T08:36:24

LCM is $225$

First find the prime factors of the two numbers. These are as follows:

$75=color(red)(3xx5)xx5$ and

$45=3xxcolor(red)(3xx5)$

Now list all the common factors. We have already listed them above in red color.

To write the Least Common Multiple (LCM), now what one needs is

to first write common factors and then add those which are not common.

Hence $LCM=color(red)(3xx5)xx5xx3=225$