The LCM of two numbers is 315. If the numbers are in the ratio 7 : 9, then the sum of the numbers is _____.

Question

Question

This question was previously asked in

RPF Constable 2024 Official Paper (Held On: 07 Mar, 2025 Shift 2)

Answer 1

Given:

LCM of two numbers = 315

Ratio of numbers = 7 : 9

Formula used:

If numbers are 7x and 9x, then LCM = (Product of numbers) ÷ HCF

Calculation:

Let numbers be 7x and 9x

⇒ Product = 7x × 9x = 63x²

HCF of 7x and 9x = x (since 7 and 9 are co-prime)

⇒ LCM = Product ÷ HCF = 63x² ÷ x = 63x

⇒ 63x = 315

⇒ x = 5

Numbers = 7 × 5 = 35 and 9 × 5 = 45

Sum = 35 + 45 = 80

∴ Sum of the numbers = 80

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