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