Grade 66 grade maths
The GCD of two numbers is 17 and their LCM is 765 how many pairs of values can the numbers assume?
The GCD of two numbers is 17 and their LCM is 765 how many pairs of values can the numbers assume?
3 Answers
Lokendra Singh
The gcd of two numbers is 17 and their LCM is 765 how many pairs of values can the number assume
Solutions
Rahul Sanapala
Given that The GCD(HCF) of two number is 17 and lcm is 765.
let the numbers be 17x and 17y
Product of the numbers = Product of LCM and HCF
17x * 17y = 765 * 17
289xy = 765*17
xy = 45
Product of the numbers = Product of LCM and HCF
17x * 17y = 765 * 17
289xy = 765*17
xy = 45
Factor pairs of 45: 5*9; 3*15
Hence the numbers
5*17 = 85
9*17 = 153
3*17 = 51
15*17 = 255
5*17 = 85
9*17 = 153
3*17 = 51
15*17 = 255
Based on the above only two pairs possible: 85 & 153; 51 & 255
Swati
Dear student,
let 17x = one of a pair of numbers
let 17y = the other number
let 17y = the other number
17x * 17y = 765
289xy = 765
simplify, divide by 17
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.
Hope this will help you out .
With Regards
Swati
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