Question

Select all pairs of numbers that have a least common multiple of 30. 3 and 65 and 6 3 and 105 and 10

Answer 1

Let's do step by step:

First case: 3 and 6. We have to factor these numbers:

`\text{Factorizing 3 : 1}*3`
`\text{Factorizing 6: 1}*2*3`

Thus the prime numbers will be 2 and 3. The Least common multiple will be:

`\text{LCM(3,6) = 2}*3\text{ = 6}`

The second case, same steps:

`\text{Factorizing 5 : 1}*5`
`\text{Factorizing 6: 1}*2*3`

Thus the prime numbers will be 2,3 and 5. The Least common multiple will be:

`LCM(5,6)\text{ = 2}*3*5=30`

Third case:

`\text{Factorizing 3 : 1}*3`
`\text{Factorizing 10 : 1}*2*5`

Thus the prime numbers will be 2,3 and 5. The Least common multiple will be:

`LCM(3,10)\text{ = 2}*3*5=30`

Last case:

`\text{Factorizing 5 : 1}*5`
`\text{Factorizing 10 : 1}*2*5`

Thus the prime numbers will be 2 and 5. The Least common multiple will be:

`LCM(5,10)\text{ = 2}*5=10`

Answer: The pairs that have a least common multiple of 30 are 5 and 6, and 3 and 10.