14 The HCF of two numbers is 6. The LCM is 72. One of the numbers is 24.
Find a possible value of the other number.
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If HCF is 6 and LCM is 72 of two numbers, then what are the two numbers?
6=2*3 and 72=2^3*3^2
Since 6 is a factor of 72, (6, 72) is an answer pair.
Having one answer makes the rest easier. Understand that the GCF is the product of the factors common to both, and the LCM is the product of the leftovers. You need to keep them apart. You can only have one 2 and one 3 on each side or else the GCF goes up.
If you move one of the 3s from the right, you get (18, 24) which works.
If you move all but one of the 2s, you also get (18, 24).
There are no other possibilities without the GCF going up. ■
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