What is the LCM of 365 and 30660?

Answer 1

LCM(365, 30660) = 2176860. But this is a wrong answer. It is a common multiple, but not the least (smallest) common multiple.

Here is how you find that out. First, factor 365 and 30660.

365 = 5 * 73

Five and seventy-three are prime (each has no divisors other than 1 and itself)

30660 = 10 * 3066 = 2 * 5 * 3066 = 2 * 5 * 3 * 1022 = 2 * 5 * 3 * 2 *511 = 2 * 5 * 3 * 2 * 7 * 73.

You may want to put these primes in order.

30660 = 2 * 2 * 3 * 5* 7 * 73.

The least common multiple will have any prime factor that is a factor as many times as it is a factor in either number, so the LCM is

2*2*3*5*7*73 = 30660.

Another way to think about this is that there are 365 days in a year, so if we didn't have leap years, then 30660 days would be an even number of years. But we do have leap years. So it isn't.