Question

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?

Answer 1

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

In the given statement is :

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.

To find what is the smallest possible value of the other integer

Now, According to the question

One of the numbers 3 ×3× 5 = 45

The lowest common multiple has to be a multiple of 45 i.e.,

3 ×3× 5 something when LCM is divided by the greatest common divisor

then the answer is 33 = 3 x 11 .

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

3 ×3× 5× 11 × ?/ some factor of 4 = 33

(3 ×5) ×3× 11 × 1 /3 × 5 = 33

So if the greatest common divisor is 3× 5 the given number is 3 ×3× 5

Hence, The smallest value of the other number will be 3 ×5× 11 =165  

Learn more about Greatest Common Divisor at:

brainly.com/question/17199530

#SPJ4