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## If x is the least common multiple of the set {6, 8, 12} and y is the greatest common factor of the set {20, 42, 72), what is the value

Question

If x is the least common multiple of the set {6, 8, 12} and y is the greatest common factor

of the set {20, 42, 72), what is the value of x/y ?

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Mathematics
6 months
2021-07-23T05:54:40+00:00
2021-07-23T05:54:40+00:00 1 Answers
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## Answers ( )

Answer:12

Step-by-step explanation:The least common multiple of {6,8,12} is 24. This can be intuitively figured by noting that any multiple of 12 is a multiple of 6 and that 12 is 1.5x larger than 8. That means we only have so multiple 12 by 2 and 8 by 3 for them to be equal. The GCF of {20,42,72} is 2 as the prime factorization of 20 is 2x2x5 and 42 is 2x3x7. That means even without having to check 72 (which is clearly even so 2 is a factor), we know that 2 is the greatest common factor that they could share. So X/Y = 24/2 = 12