Juan has three rain sticks measuring 8 inches, 6 inches, and 12 inches each. what is the least common multiple of 8, 6, and 12?
A.12
B.24***
C.48
D.96
is it B?
agree
Yes, it is B. The least common multiple (LCM) of 8, 6, and 12 is 24.
Yes, you are correct. The least common multiple (LCM) of 8, 6, and 12 is indeed 24, which corresponds to option B.
To find the least common multiple of these three numbers, you can follow these steps:
1. Determine the prime factorization of each number:
- The prime factorization of 8 is 2 * 2 * 2.
- The prime factorization of 6 is 2 * 3.
- The prime factorization of 12 is 2 * 2 * 3.
2. Take the highest exponent for each prime factor:
- For the prime factor 2, the highest exponent is 3 (from the prime factorization of 8 and 12).
- For the prime factor 3, the highest exponent is 1 (from the prime factorization of 6).
3. Multiply these prime factors with their highest exponents:
- 2^3 * 3^1 = 8 * 3 = 24.
Therefore, the least common multiple of 8, 6, and 12 is 24.