What is the LCM of 75 500 90?

Answer 1

To find the LCM of 2 or more numbers, express the numbers in the prime composition using power notation, and then use the highest power of each prime across the numbers:

75 = 3 x 5 x 5 = 20 x 31 x 52

500 = 2 x 2 x 5 x 5 x 5 = 22 x 30 x 53

90 = 2 x 3 x 3 x 5 = 21 x 32 x 51

LCM = 22 x 32 x 53 = 4500

The power of the prime tells how many are there, so 22 means there are 2 and is the same as 2 x 2, 53 = 5 x 5 x 5.

Where there are none, the power is 0; any number to the power 0 is 1, so 20 = 30 = 50 = 1.

So 75 = 20 x 31 x 52 = 1 x 3 x 5 x 5.