Q. The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is = ?
✅ Correct Answer: (A)
10
Explanation: LCM = 495
HCF = 5 ( given )
∴ Let numbers are = 5x and 5y
∴ LCM = 5xy
⇒ 5xy = 495
⇒ xy = 99
∴ Possible co-prime factors are
1, 99
9, 11
∴ Possible numbers are 5x, 5y
45, 55
5, 495
Now given that sum of numbers = 100
So, required numbers are = (45, 55)
∴ Difference of numbers = 55 - 45 = 10
HCF = 5 ( given )
∴ Let numbers are = 5x and 5y
∴ LCM = 5xy
⇒ 5xy = 495
⇒ xy = 99
∴ Possible co-prime factors are
1, 99
9, 11
∴ Possible numbers are 5x, 5y
45, 55
5, 495
Now given that sum of numbers = 100
So, required numbers are = (45, 55)
∴ Difference of numbers = 55 - 45 = 10
Explanation by: Mr. Dubey
LCM = 495
HCF = 5 ( given )
∴ Let numbers are = 5x and 5y
∴ LCM = 5xy
⇒ 5xy = 495
⇒ xy = 99
∴ Possible co-prime factors are
1, 99
9, 11
∴ Possible numbers are 5x, 5y
45, 55
5, 495
Now given that sum of numbers = 100
So, required numbers are = (45, 55)
∴ Difference of numbers = 55 - 45 = 10
HCF = 5 ( given )
∴ Let numbers are = 5x and 5y
∴ LCM = 5xy
⇒ 5xy = 495
⇒ xy = 99
∴ Possible co-prime factors are
1, 99
9, 11
∴ Possible numbers are 5x, 5y
45, 55
5, 495
Now given that sum of numbers = 100
So, required numbers are = (45, 55)
∴ Difference of numbers = 55 - 45 = 10