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The GCD of two numbers is 17 and their L...

The GCD of two numbers is 17 and their LCM is 765. How many pairs of values can the numbers assume?

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
If the GCD of two numbers is 17 , then the numbers are in the form of 17x and 17y (where x and y are co-primes).
`17xy =765 `
`xy=(765)/(17) =45`
`xy=45=9xx5`
`therefore` The numbers can be `17xx9=153` and `17xx5=85`.
Or.
The numbers can be `17xx1=17 and 765`
`therefore` Two pairs are possible.
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