Question

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

Answer 1

5 and 6  and 3 and 10, the pairs of numbers that have a least common multiple of 30.

Step-by-step explanation:

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