Why is 145 not a LCM of 15 and 18?

Answer 1

There is only one LCM, so it cannot be A lcm, but possibly THE lcm.

The LCM of any two (or more) numbers MUST be a multiple of all the numbers.

For 15 and 18 the LCM must be a multiple of both 15 and 18.

In particular it must be one of the multiples of 18.

18 is an even number, so all its multiples will be even.

145 is an odd number, so it cannot be a multiple of 18

Thus 145 cannot be a multiple of both 15 and 18.

Thus it cannot be the LCM of 15 and 18.

QED.