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: [tex]1 \times 3[/tex]
Prime factorization of 6: [tex]2 \times 3[/tex]
Using all prime numbers found as often as each occurs most often we take
[tex]2 \times 3=6[/tex]
Therefore LCM (3, 6) = 6.
Case 2: LCM (5, 6)
Prime factorization of 5: [tex]1 \times 5[/tex]
Prime factorization of 6: [tex]2 \times 3[/tex]
Using all prime numbers found as often as each occurs most often we take
[tex]5 \times 2 \times 3=30[/tex]
Therefore LCM (5, 6) = 30
Case 3: LCM (3, 10)
Prime factorization of 3: [tex]1 \times 3[/tex]
Prime factorization of 10: [tex]2 \times 5[/tex]
Using all prime numbers found as often as each occurs most often we take
[tex]5 \times 2 \times 3=30[/tex]
Therefore LCM (3, 10) = 30
Case 4: LCM (5, 10)
Prime factorization of 5: [tex]1 \times 5[/tex]
Prime factorization of 10: [tex]2 \times 5[/tex]
Using all prime numbers found as often as each occurs most often we take
[tex]5 \times 2=10[/tex]
Therefore LCM (5, 10) = 10
