What is the greatest common multiple of 60 and 36?

Answer 1

The greatest common multiple of 36 and 60 is the largest number divisible by both 36 & 60 and is infinite; there is no greatest common multiple - what ever multiple you come up with as the greatest I can always add 2160 and get an even larger multiple of 36 & 60.

I suspect you meant:

• What is the greatest common factor of 36 and 60?

This is the largest number that is a factor of (that is divides exactly into) both 36 and 60; it is 12

36 = 22 x 32

60 = 22 x 3 x 5

gcf = 22 x 3 = 12

or

• What is the lowest common multiple of 36 and 60?

This is the smallest number that 36 and 60 both divide into; it is 180

36 = 22 x 32

60 = 22 x 3 x 5

lcm = 22 x 32 x 5 = 180

Answer 2

There is really no such thing as a "greatest common multiple". Once you find the least common multiple of a set of numbers, you can keep adding the LCM to itself over and over again. Each new number you get will be a common multiple of your set of numbers, but each new number will always be larger than the previous. This means that you can keep adding while the number approaches infinity and you will still never find a greatest multiple.

Answer 3

The greatest common multiple of any set of integers is infinite.