Two numbers in a 3:4 ratio have an H.C.F of 4. What is their L.C.M__________?
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Answer: D. 48
Explanation
Multiplying the ratio terms three and four by the highest common factor four gives twelve and sixteen. Alternatively multiplying the ratio product by the HCF directly yields the least common multiple. Calculating three multiplied by four multiplied by four produces the final LCM of forty eight. The least common multiple of numbers given in a ratio equals the product of the ratio terms multiplied by HCF. The HCF represents the fundamental common divisor shared by both proportional numbers. Multiplying ratio components by their highest common factor recovers the original number values.
Number theory calculations involving ratios and LCM are common in mathematical aptitude tests. Scheduling and frequency synchronization problems utilize LCM principles to determine overlap points. Understanding proportionality helps simplify complex arithmetic and algebraic problem sets. Option A suggests twelve which represents only the first calculated number rather than the LCM. Option B suggests sixteen which represents only the second calculated number in the ratio. Option C suggests twenty four which underestimates the full least common multiple calculation.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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