Question

1. 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) 2. The LCM of two numbers is 1024 and one of them is a prime number. Find their GCD.
(a) 3 (b) 2 (c) 5 (d) 7
if u answer these questions then I will mark ur answer as a brainlist

Answer 1

Both of them can assume 2 values.

let 17x = one of a pair of numbers
let 17y = the other number

17x * 17y = 765
289xy = 765
simplify, divide by 17


xy = 45
Factor pairs of 45: 5*9; 3*15
therefore the numbers
5*17 = 85
9*17 = 153
and
3*17 = 51
15*17 = 255

I can find two pairs: 85 & 153; 51 & 255.

Similarly , the other one also can assume 2 pairs.

Answer 2

, your answer is truly helpful Sir but I have one doubt as I cross checked it with the RD Sharma book of class 6th there it is written like one more fear is possible of 1 and 45 like if we want to find the factor pairs of 45 we can split it into 1 and 45 so in that case I believe there are three pairs of 45 or as factors of 45, kindly cross check the answer of two pairs because I believe it is three pairs.

But defenitely with your help i am able to reach this conclusion (which i am not sure is true). Tge solution you provided was a great help