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Q.

The greatest common divisor of two numbers is Question Image and their least common multiple is Question Image. How many pairs of values can the numbers assume?

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a

1

b

2

c

3

d

4 

answer is B.

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Detailed Solution

Concept- The least common multiple is indeed the smallest number that is exactly divisible by each of the given numbers, and the highest common factor is indeed the largest number that divides two or more numbers (HCF).
Here the GCD of numbers is 17.
Then, the numbers are Question Image and Question Image, where a and b are relatively prime.
Given that Question ImageQuestion ImageQuestion ImageQuestion ImageThus, the numbers are Question Image and Question Image.
The numbers can be Question Image and 765.
Therefore, we have two pairs.
Hence, the correct answer is option 2.
 
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The greatest common divisor of two numbers is and their least common multiple is . How many pairs of values can the numbers assume?