The least common multiple (LCM) of 7, 9, and 21 is 63.
To find the LCM, we can use the method of prime factorization:
- 7 is already a prime number, so it can be factored as: 7
- 9 can be factored into primes as: 3 x 3 or 3²
- 21 can be factored into primes as: 3 x 7
Now, we take the highest power of each prime number that appears in the factorizations:
- For prime 3, the highest power is 3² (from 9).
- For prime 7, the highest power is 7 (from 7 and 21).
Thus, the LCM is calculated as:
LCM = 3² x 7 = 9 x 7 = 63
So, the least common multiple of 7, 9, and 21 is 63.