What is the LCM of 10, 15, 20 and 30?

Question

Roman Alvarez · Accepted Answer

#60#

First, write out the prime factorization of each number

We can rewrite the above with more clarity as

For each prime factor, take the one with the highest exponent. 2 is raised to the power of 2 in 20. 3 and 5 have both a maximum exponent of 1. Refer to the #color(blue)("blue")# colored exponents above.

Therefore,

#"LCM" = 2^2 xx 3^1 xx 5^1#

#= 60#

This algorithm is guaranteed to generate the least common multiple.

Emery Allen · Answer

#LCM = 60#

The first thing to notice is that we do not need to consider #10 and 15# at all because they are factors of #20 and 30# respectively.

We only need to find the LCM of #color(blue)(20 and 30)#

You should be very familiar with these two numbers and their multiples.

The quickest and easiest method is to consider the multiples of the bigger one (#30)#, until you find the first one which is a multiple of #20#.

The multiples of #30# are: #30, color(magenta)(60), 90, 120 ...# #color(white)(wwwwwwwwww.wwwww)uarr# #color(white)(wwwwwwwwww.wwww)20 xx3#

#60# is the multiple we need. It is divisible by #10,15,20 and 30#

If the given numbers had been bigger or with less obvious factors and multiples, then I would have used the method of prime factors, but this one can be found mentally.

Jeremiah Andrews · Answer

undefined The LCM (Least Common Multiple) of 10, 15, 20, and 30 is 60.