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

##60##

First, write out the prime factorization of each number

• ##10 = 2 xx 5##
• ##15 = 3 xx 5##
• ##20 = 2^2 xx 5##
• ##30 = 2 xx 3 xx 5##

We can rewrite the above with more clarity as

• ##10 = 2^1 xx 3^0 xx 5^color(blue)(1)##
• ##15 = 2^0 xx 3^color(blue)(1) xx 5^color(blue)(1)##
• ##20 = 2^color(blue)(2) xx 3^0 xx 5^color(blue)(1)##
• ##30 = 2^1 xx 3^color(blue)(1) xx 5^color(blue)(1)##

For each prime factor, take the one with the highest above.

Therefore,

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

##= 60##

This algorithm is guaranteed to generate the .