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# Interesting math Question (Number Theory)

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When the least common multiple of two positive integers is divided by their greatest common divisor, the result is 33. If one integer is 45, what is the smallest possible value of the other integer?

Nov 6, 2019

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There is probably some good technique to use.

I just found it by playing with the numbers .

One of the numbers is 3*3*5 = 45

The lowest common multiple has to be a multiple of 45         that is   3*3*5*something

when LCM is divided by the greatest common divisor then the answer is 33

33=3*11

So the other number will have to be a multiple of 11

$$\frac{3*3*5*11*?}{\text{some factor of 45}}=33\\ \frac{(3*5)*3*11*1}{3*5}=33\\$$

So if the greatest common divisor is 3*5

The given number is    3*3*5

The smallest value of the other number will be  3*5*11 = 165

Nov 6, 2019