What is the least common multiple of 20 and 60 and 12?

Answer 1

LCM(Least Common Multiple) of a, b & c is a if both b & cdivide a.

Here both 20 and 12 divide 60 therefore, LCM(20, 60 and 12) = 60.

Alternate method:

The above method is a special case. Now, we apply the general method which is useful for small numbers but it can be difficult even for small numbers. But, without considering the difficulty we apply it.

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120,...

Multiples of 20: 20, 40, 60, 80, 100, 120, 140,...

Multiples of 60: 60, 120, 180, 240, 300, 360,...

Common multiples are 60, 120 and so on. There exists infinitely many common multiples but, the least common multiple is only one which is, here, 60.

Here, we can see clearly that writing all the multiples requires a lot of work and it is difficult to find LCM of larger numbers.

There is another method we can apply and it is considered the best method for finding LCM.

See related links below to know more about another method

Answer 2

60