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
Six bells begin to toll together and toll, respectively, at intervals of 3, 4, 6, 7, 8 and 12 seconds. After how many seconds, will they toll together again?
A and B are two prime numbers such that A > B and their LCM is 209. The value of A 2 - B is:
Find the least number which when divided by 12, 18, 24 and 30 leaves 4 as remainder in each case, but when divided by 7 leaves no remainder.
Calculate the HCF of \(\frac{12}{5}\) , \(\frac{14}{15}\) and \(\frac{16}{17}\) .
Three numbers are in the proportion of 3 : 8 : 15 and their LCM is 8280. What is their HCF?
