The GCD of two numbers is 17 and their LCM is 765 how many pairs of values can the numbers assume?
Lokendra Singh , 5 Years ago
Grade 6
6 grade maths> The GCD of two numbers is 17 and their LC...
3 AnswersLokendra Singh
Last Activity: 5 Years ago
The gcd of two numbers is 17 and their LCM is 765 how many pairs of values can the number assume
Solutions
Rahul Sanapala
Last Activity: 5 Years ago
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
Last Activity: 4 Years ago
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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