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Question

The HCF of 2472, 1284 and a third number 'N' is 12. If their LCM is 23×32×51×103×107, then the number 'N' could be:

A
22×32×71
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B
22×33×103
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C
22×32×51
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D
None of these
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Solution

The correct option is C 22×32×51
2472=23×103×3; 1284=22×107×3. Since the HCF is 12, the number must have a component of 22×3 at the very least in it. Also, since the LCM is 23×32×51×103×107. We can see that the minimum requirement in the required number has to be 32×51. Combining these two requirements we get that the number should have 22×32×51 at the minimum and the power of 2 could also be 23 while we could also have either one of 103 and/or 107 as a part of the required number.
Thus, for instance, the number could also be 23×32×51×1031×1071. The question has asked us what 'could' the number be?
Option (c) gives us a possible value of the number and is hence the correct answer.

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