factor them first:
75 = 3 * 5 * 5
90 = 2 * 3 * 3 * 5
Take out the parts common to both of them from just one of them. There's a 3 and a 5 in both, so take a 3 and a 5 out of the first one. Leave the other one alone.
3 * 5 * 5 >> 5
2 * 3 * 3 * 5 >> 2 * 3 * 3 * 5
multiply the remaining stuff from both together
5 * 2 * 3 * 3 * 5 = 450
the least common multiple of 75 and 90 is 450