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# How Given any two numbers which is greater the LCM of the numbers or. The GCF of the numbers why?

Wiki User

2017-09-19 15:20:26

The LCM will never be less than the GCF. To be a multiple of both numbers, the LCM will have to be equal to or greater than the larger number. To be a factor of both numbers, the GCF will have to be equal to or less than the smaller number.

The only problem comes when you're comparing a number to itself. The LCM of 10 and 10 is 10. The GCF of 10 and 10 is 10.

Wiki User

2017-09-19 15:20:26
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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Wiki User

2017-09-15 12:44:51

The LCM is at least as great. The LCM is a multiple of the two numbers and so must be at least as large as the two numbers. Consequently it must be at least as large as the larger of the two numbers. On the other hand, the GCF is a factor of the two numbers and so must be at most as large as the two numbers. Consequently it must be at most as large as the smaller of the two numbers. Combining these inequalities shows that the LCM must be at least as great as the GCF.