Question

When the greatest common divisor and least common multiple of two integers are multiplied, the product is 180. How many different values could be the greatest common divisor of the two integers

Answer 1

The different values that could be be the greatest common divisor of the two integers are; 1, 2, 3, 4, 6

How to find the greatest common divisor?

Let the numbers be a, b. Thus, the product of the GCD(a, b) and the LCM(a, b) will be ab.

Now, for us to get something to be a factor of the GCD we need to make it be a factor of both a, b. Thus, its' square must be a factor of 180.

Therefore, the only numbers whose square is a factor of 1800 are 1, 2, 3, 4, 6 and as such they are the only GCDs possible.

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