Question:
Three numbers are in the ratio of $3 : 4 : 5$ and their L.C.M is 2400. Their H.C.F is:
Three numbers are in the ratio of $3 : 4 : 5$ and their L.C.M is 2400. Their H.C.F is:
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For numbers in ratio, LCM = (LCM of ratio numbers) × common factor.
Updated On: Apr 23, 2026
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The Correct Option is A
Solution and Explanation
Concept:
Let numbers be $3x, 4x, 5x$.
Step 1: LCM of numbers.
\[ {LCM} = x \times {LCM}(3,4,5) \] \[ {LCM}(3,4,5) = 60 \] \[ \Rightarrow 60x = 2400 \Rightarrow x = 40 \]
Step 2: HCF of numbers.
\[ {HCF} = x = 40 \]
Hence, the H.C.F is 40.
Step 1: LCM of numbers.
\[ {LCM} = x \times {LCM}(3,4,5) \] \[ {LCM}(3,4,5) = 60 \] \[ \Rightarrow 60x = 2400 \Rightarrow x = 40 \]
Step 2: HCF of numbers.
\[ {HCF} = x = 40 \]
Hence, the H.C.F is 40.
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