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 HCF and LCM of two numbers are 12 and 72, respectively. If the ratio of the two numbers is 2 ∶ 3, then the larger of the two numbers is:
Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.
Joseph visits the club on every 5 th day, Harsh visits on every 24 th day, while Sumit visits on every 9 th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?
What is the least number which when divided by 12,20 and 24 leaves in each case a remainder of 8?
Which of the following is a pair of co-primes?
