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The LCM of two numbers is fourteen times their HCF, and HCF + LCM = 600. One of the numbers is 280. Find the other.

Competition practiceNumber System, HCF & LCM

A80
B40
C560
D160

Step-by-Step Solution

Let HCF =

h

, so LCM = 14

h

and

15 h = 600, h = 40

, LCM = 560. Other number =

40 \times 560 \div 280 = 80

. (Check: HCF(80, 280) = 40, LCM = 560.)

Answer: A) 80

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