an integer x written as a product of its prime factor is ( a to the power of 2 * 7 to the power b + 2) . an integer Y written as a product of its prime factor is ( a to the power of 3 * 7 to the power of 2) the highest common factor of X and Y is 1225. the lowest common multiple of X and Y is 42875. what is the value of X and Y.
Answers
sorry boys I don't know if I will put comment that I have to search on this it's a good quite complicated questions of the Year
Answer:
X=8575
Y=6125
Step-by-step explanation:
I know I'm late but i'm putting this up just incase someone has troubles on solving the question too :D
HCF of X and Y is 1225
you take the smallest exponent that the prime number are both present in both numbers, in this case:
a^2 from X, and 7^2 from Y ---> we're solving for A
a^2 x 7^2 = 1225
a^2 x 49 = 1225
a^2 = 25
a = sqrt of 25
a = 5
LCM of X and Y is 42875
you take the biggest exponent! - we don't care if it doesn't reoccur in other number, in this case:
5^3 x 7^b+2 = 42875
125 x 7^b+2 = 42875
7^b+2 = 343 --> make 343 having the same root number of 7
7^b+2 = 7^3 --> remove the 7s, just to have the exponents
b+2 = 3
b = 1
SO now,
X: 5^2 x 7^3 = 8575
Y: 5^3 x 7^2 = 6125
i hope it helps :) and i'm sorry if i don't explain it too clearly