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11Alexandr11 [23.1K]
3 years ago
10

Select all pairs of numbers that have a least common multiple of 30.

Mathematics
1 answer:
ddd [48]3 years ago
8 0

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:  1 \times 3

Prime factorization of 6:  2 \times 3

Using all prime numbers found as often as each occurs most often we take

               2 \times 3=6

Therefore LCM (3, 6) = 6.

Case 2: LCM (5, 6)

Prime factorization of 5:  1 \times 5

Prime factorization of 6:  2 \times 3

Using all prime numbers found as often as each occurs most often we take

                     5 \times 2 \times 3=30

Therefore LCM (5, 6) = 30

Case 3: LCM (3, 10)

Prime factorization of 3:  1 \times 3

Prime factorization of 10:  2 \times 5

Using all prime numbers found as often as each occurs most often we take

                    5 \times 2 \times 3=30

Therefore LCM (3, 10) = 30

Case 4: LCM (5, 10)

Prime factorization of 5:  1 \times 5

Prime factorization of 10: 2 \times 5

Using all prime numbers found as often as each occurs most often we take

                       5 \times 2=10

Therefore LCM (5, 10) = 10

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