Three numbers are in the ratio 3:4:5 and their L.C.M is 2400. Their H.C.F is:
Correct answer: A. 40
- A. 40
- B. 80
- C. 120
- D. 200
Explanation
Write the numbers as 3x, 4x and 5x. Since 3, 4 and 5 are pairwise coprime, their LCM is 3 x 4 x 5 x = 60x; hence 60x = 2400, so x = 40. Their HCF is therefore 40. The likely mistake is choosing 80 by taking an incomplete common factor from the LCM calculation.
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About Ratio and Proportion
Ratios compare quantities in the same units, while proportions state that two ratios are equal. Problems cover simplification, division in a given ratio, direct and inverse variation, scale, and missing terms, with attention to the difference between a ratio and a fraction representing part of a whole.
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