Respuesta :
Let's do step by step:
First case: 3 and 6. We have to factor these numbers:
[tex]\text{Factorizing 3 : 1}\times3[/tex][tex]\text{Factorizing 6: 1}\times2\times3[/tex]Thus the prime numbers will be 2 and 3. The Least common multiple will be:
[tex]\text{LCM(3,6) = 2}\times3\text{ = 6}[/tex]The second case, same steps:
[tex]\text{Factorizing 5 : 1}\times5[/tex][tex]\text{Factorizing 6: 1}\times2\times3[/tex]Thus the prime numbers will be 2,3 and 5. The Least common multiple will be:
[tex]LCM(5,6)\text{ = 2}\times3\times5=30[/tex]Third case:
[tex]\text{Factorizing 3 : 1}\times3[/tex][tex]\text{Factorizing 10 : 1}\times2\times5[/tex]Thus the prime numbers will be 2,3 and 5. The Least common multiple will be:
[tex]LCM(3,10)\text{ = 2}\times3\times5=30[/tex]Last case:
[tex]\text{Factorizing 5 : 1}\times5[/tex][tex]\text{Factorizing 10 : 1}\times2\times5[/tex]Thus the prime numbers will be 2 and 5. The Least common multiple will be:
[tex]LCM(5,10)\text{ = 2}\times5=10[/tex]Answer: The pairs that have a least common multiple of 30 are 5 and 6, and 3 and 10.
