# 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?

The other number is

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.

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The second number would be the product of 45 and 12

540

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

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we have

we have the well known relationship

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To find the other number, we can use the relationship between the LCM and GCF of two numbers.

The relationship between the LCM (Least Common Multiple) and GCF (Greatest Common Factor) of two numbers (a) and (b) is given by the formula:

[ \text{LCM}(a, b) \times \text{GCF}(a, b) = |a \times b| ]

Given that one of the numbers is (84), we can plug the given values into the formula:

[ 3780 \times 12 = 84 \times \text{other number} ]

Now, we can solve for the other number:

[ \text{other number} = \frac{3780 \times 12}{84} ]

[ \text{other number} = \frac{45360}{84} ]

[ \text{other number} = 540 ]

Therefore, the other number is (540).

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