The HCF of two numbers is one-twentieth of their LCM. If one of the numbers is 96 and the difference of the LCM and the HCF is 456, then what is the other number?
120
Concept Used:
LCM × HCF = Product of two numbers
Calculation:
According to the question,
HCF = 1/20 × LCM …(i)
LCM - HCF = 456
⇒ LCM - (1/20 × LCM) = 456 [From equation (i)]
⇒ 19/20 × LCM = 456
⇒ LCM = (456 × 20)/19
⇒ LCM = 480
Then HCF = (480 - 456) = 24
Let the other number be k
k × 96 = 24 × 480
⇒ k = 11520/96
⇒ k = 120
∴ The correct answer is 120.
Important Questions from LCM and HCF
The greatest three-digit number which is divisible by 14, 28, and 42 is:
What is the greatest number that will divide 209 and 347 leaving remainder 5 and 7 respectively?
A number is three times another number and their HCF is 8. What is the sum of the squares of the numbers?
The HCF of 2091, 3485 and 4879 is x. The sum of the digits of x is:
If three numbers are in ratio of 3 : 5 : 7 and their LCM is 2415, what is the difference between the second number and the first number?
