Find the lcm of 21 and 9

List out the prime factorization of each number

21 = 3*7

9 = 3*3

We see that the unique prime factors are: 3, 7

The factor 3 happens at most two times, while 7 only shows up one time. Multiply this out: 3*3*7 = 9*7 = 63

Therefore the LCM is 63

As a check, list out the multiples of each number

multiples of 21 are: 21, 42, 63, 84, 105, 126, ...

multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, ...

we see that 63 shows up in the list and it is the smallest number in common between the two lists; confirming we have the proper LCM of 63

The answer of lcm is 63