Why is 420 the LCM of 1 12 30 84?

Answer 1

Because any smaller positive integer cannot be divided by all the above numbers without remainder.

In fact, the presence of 1, when calculating an LCM makes no difference since it will go into any integer. Also, since 12 is a factor of 84, 12 will go into any number that 84 goes into. So the presence of 12 is also irrelevant. Thus, for determining the LCM, only 30 and 84 matter.

Answer 2

Because 420 is the smallest positive integer that all of those numbers divide into evenly with no remainder.