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Which is a way to use prime factorization to find the least common multiple of 8 and 6?
6 ➔ 2 × 3
8 ➔ 2 × 2 × 2
LCM = 2 × 2 × 2 × 3
= 24
6 ➔ 2 × 3
8 ➔ 2 × 2 × 2
LCM = 2 × 2 × 2 × 2 × 3
= 48
6 ➔ 2 × 3
8 ➔ 2 × 2 × 2
LCM = 2
= 2
6 ➔ 2 × 3
8 ➔ 2 × 2 × 2
LCM = 2 × 2 × 3
= 12
To find the least common multiple (LCM) of 8 and 6 using prime factorization, we first express each number in terms of its prime factors:
– 6 ➔ 2 × 3
– 8 ➔ 2 × 2 × 2
To find the LCM, we take the highest power of each prime factor present in the factorizations:
– The highest power of 2 is (2^3) (from 8).
– The highest power of 3 is (3^1) (from 6).
Now, we multiply these together:
(LCM = 2^3 × 3^1 = 8 × 3 = 24).
So the correct answer is:
LCM = 2 × 2 × 2 × 3 = 24.