Question

Find the LCM (least common multiple) of 63 and 84.
LCM =

Answer 1

The Least Common Multiple (LCM) of 63 and 84 is 252, found by using prime factorization to take the highest power of each prime factor appearing in either number.

Step-by-step explanation:

To find the Least Common Multiple (LCM) of 63 and 84, we can use prime factorization:

1. First, we find the prime factors of each number.
   63 = 3 × 3 × 7
   84 = 2 × 2 × 3 × 7
2. Next, for each prime factor, take the highest power that appears in either number.
   In this case, we have:
   2 squared (because 2 × 2 is the highest power of 2),
   3 squared (because 3 × 3 is the highest power of 3),
   and 7 (since 7 appears to the first power in both).
3. Now, multiply these together to get the LCM:
   LCM = 2² × 3² × 7 = 4 × 9 × 7 = 36 × 7 = 252

The LCM of 63 and 84 is 252.