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Three numbers are in the ratio 3 : 4 : 5, and their LCM is 2400. What is their HCF?

Q: Three numbers are in the ratio 3 : 4 : 5, and their LCM is 2400. What is their HCF?

Concept / Approach If numbers are in ratio 3:4:5 and their HCF is h, the numbers are 3h, 4h, and 5h. Then LCM = h × LCM(3,4,5). Step-by-step calculation LCM(3,4,5) = 60Given LCM = 2400 = h × 60h = 2400 ÷ 60 = 40 Final Answer 40

Difficulty: Easy

Correct Answer: 40

Explanation:

Concept / Approach

If numbers are in ratio 3:4:5 and their HCF is h, the numbers are 3h, 4h, and 5h.
Then LCM = h × LCM(3,4,5).

Step-by-step calculation
LCM(3,4,5) = 60Given LCM = 2400 = h × 60h = 2400 ÷ 60 = 40

Final Answer
40

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