Find the LCM of Three Numbers: 8, 14, and 20

Question

Find the least common multiple (LCM) of these numbers:

8   14   20 \boxed{8} ~~~ \boxed{14} ~~~ \boxed{20}

Step-by-Step Solution

To find the least common multiple (LCM) of 8, 14, and 20, determine their prime factorization:

Prime factors of 8: 8=23 8 = 2^3

Prime factors of 14: 14=21×71 14 = 2^1 \times 7^1

Prime factors of 20: 20=22×51 20 = 2^2 \times 5^1

The LCM is the product of the highest powers of all prime factors:

23×71×51=8×35=280 2^3 \times 7^1 \times 5^1 = 8 \times 35 = 280

Answer

280

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Common denominator

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Common Denominators: More than two fractions Common Denominators: The common denominator is smaller than the product of the denominators