Question
Download Solution PDFThe HCF of two numbers is 9 and their LCM is 252. The sum of numbers is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
HCF = 9, LCM = 252
Concept:
LCM = Least common multiple (Lease value divisible by all the given numbers)
HCF = highest common factor (Highest value which will exactly divide all the given numbers)
Formula Used:
LCM × HCF = Product of numbers
Calculation:
Let, the numbers be 9x and 9y where x and y are co-prime
According to the question,
9x × 9y = 252 × 9
⇒ xy = 28
Possible values of (x, y) are (1, 28), (28, 1), (4, 7) and (7, 4)
Case 1: For (x, y) is (1, 28) or (28, 1)
The numbers are = (9 × 1) = 9 and (9 × 28) = 252
⇒ Sum of the numbers = (9 + 252) = 261
Case 2: For (x, y) is (4, 7) or (7, 4)
The numbers are = (9 × 4) = 36 and (9 × 7) = 63
⇒ Sum of the numbers = (36 + 63) = 99
∵ 261 is not in options,
∴ Required sum = 99Last updated on Jul 15, 2025
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