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least common multiple

the smallest positive integer that is divisible by two numbers. to find the lcm: method 1: list the prime factors of each number and multiply each factor by the greatest number of times it occurs in either number. method 2: list the multiples of a number and find the first one that is the same.

example for method 1: the lcm of 8 (2 × 2 × 2) and 14 (2 × 7) is 56 (2 × 2 × 2 × 7). example for method 2: 8: 8, 16, 24, 32, 40, 48, 56. 14: 14, 28, 42, 56. so the lcm is 56.

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