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5 and 6 and 3 and 10, the pairs of numbers that have a least common multiple of 30.
<u>Step-by-step explanation:</u>
Case 1: LCM (3, 6)
Prime factorization of 3:
Prime factorization of 6:
Using all prime numbers found as often as each occurs most often we take
Therefore LCM (3, 6) = 6.
Case 2: LCM (5, 6)
Prime factorization of 5:
Prime factorization of 6:
Using all prime numbers found as often as each occurs most often we take
Therefore LCM (5, 6) = 30
Case 3: LCM (3, 10)
Prime factorization of 3:
Prime factorization of 10:
Using all prime numbers found as often as each occurs most often we take
Therefore LCM (3, 10) = 30
Case 4: LCM (5, 10)
Prime factorization of 5:
Prime factorization of 10:
Using all prime numbers found as often as each occurs most often we take
Therefore LCM (5, 10) = 10