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No. It can be neither.

HCF is Highest Common Factor; a factor of a number is a number which divides into it with no remainder. Thus all factors are less than or equal to the number. 72 is greater than 6, therefore it cannot be a factor of 6, nor the Highest Common Factor of 6 and another number.

LCM is Lowest Common Multiple; a multiple of a number is that number times some other number. Thus all multiples are greater than or equal to the number. 72 is less than 252, therefore it cannot be a multiple of 252, nor can it be the Lowest Common Multiple of 252 and another number.

However, 6 is a factor of 72, thus 6 could be the HCF of 72 and another number, eg hcf(30, 72) = 6.

But 252 is not a multiple of 72, so 252 could not be a LCM of 72 and some other number.

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Q: Is 72 a hcf of six and LCM of 252?
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