What is the least common multiple of #2#, #3# and #5# ?

2 Answers
Tony B
Oct 16, 2017

Showing you how to reason it out without having to do loads of calculations.

Explanation:

Any multiple of 5 will have as the last digit either 0 or 5.

The value of 5 is odd. Consequently any number with the last digit of 5 must also be odd. Thus 2 will not divide into any number that has 5 as the last digit. That only leaves a number with the last digit being 0.

20 is exactly divisible by 5 but not 3
30 is divisible by all.

So the Least Common Multiple (LCM) is 30.

George C.
Oct 19, 2017

The least common multiple of #2#, #3# and #5# is #30#.

Explanation:

The numbers #2#, #3# and #5# are distinct prime numbers, so they have no common factor larger than #1#.

As a result, the least number which is a multiple of all of them is their product:

#2 * 3 * 5 = 30#

More generally, given any list of numbers you can find their least common multiple by finding the least common multiple of the first pair of numbers, then the least common multiple of that and the next number, etc.

So in our example, the least common multiple of #2# and #3# is #2*3 = 6# (since #2# and #3# have no common factor larger than #1#). Then the least common multiple of #6# and #5# is #6 * 5 = 30# (since #6# and #5# have no common factor larger than #1#).

To find the least common multiple of two composite numbers you can either factor them first and combine the distinct factors or find their greatest common factor (GCF) by some other means and divide their product by that.

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