# There are two numbers. One of them is 84. Their Lowest Common Multiple (LCM) is 3780 and their Greatest Common Factor (GCF) is 12. What is the other number?

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The other number is

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For any questions involving HCF and LCM,find each number as the product of the prime factors. That will tell you what you are working with.

The other number cannot have

The other number is therefore

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Describe your changes (optional) 200

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we have

to find

we have the well known relationship

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The second number would be the product of 45 and 12

540

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Dividing 3780 by 84 gives one of the common factors of 84 and the second number.

The HCF = 12 so the second number has factors of 45 and 12

Describe your changes (optional) 200