# The LCM of two different numbers is 18, and the GCF is 6. What are the numbers?

The numbers themselves are 6 and 18.

Each number could be 1, 2, 3, 6, 9, or 18 if the LCM of the two numbers is 18. This implies that both numbers must be factors of 18.

Both numbers are divisible by six if their GCF is six. As a result, any number could be 6, 12, 18, 24,..., etc.

So we get

This method is always effective. However, for the numbers 6 and 18, which coincidentally happened to be the GCF and LCM already, it was not required nor particularly helpful.

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They must have the prime factors

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To find the numbers given their least common multiple (LCM) and greatest common factor (GCF), you can use the relationship between the LCM, GCF, and the actual numbers.

If ( a ) and ( b ) are the two numbers, then:

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

Given that the LCM is 18 and the GCF is 6, we can substitute these values into the equation:

[ 18 \times 6 = a \times b ]

[ 108 = a \times b ]

Now, we need to find two numbers that multiply to give 108 and whose GCF is 6. The pairs of numbers that meet this condition are 9 and 12.

So, the numbers are 9 and 12.

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