| | Question 3

The LCM of two numbers is 15 times of HCF. The sum of HCF and LCM is 480. If both number are smaller than LCM. Find both the numbers.
(A) 60 and 90
(B) 90 and 120
(C) 120 and 150
(D) 90 and 150


Answer: (D)

Explanation: LCM = 15 * HCF
We know that
LCM + HCF = 480
16 * HCF = 480
HCF = 30
Then LCM = 450
LCM = 15 HCF
30 * x * y = 15 * 30
x * y = 15
Factors are {1 x 15} and { 3 x 5}
Both numbers less than LCM so take {3 x 5}
Hence numbers are 3 * 30 = 90 and 5 * 30 = 150

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