Discussion
If two positive numbers are in the ratio 3 : 5 and their least common multiple is 105, then the numbers are respectively
Answer: B
The numbers are 21 and 35.
Let the numbers be 3k and 5k. Since 3 and 5 have no common factor, their LCM is 15k:
\[ \begin{aligned} 15k &= 105 \\ k &= 7 \end{aligned} \]
So the numbers are 21 and 35. Check: \(21 = 3 \times 7\) and \(35 = 5 \times 7\), so their LCM is \(3 \times 5 \times 7 = 105\), and their HCF is the common factor 7. The pairs 15, 25 (LCM 75), 27, 45 (LCM 135) and 9, 15 (LCM 45) are also in the ratio 3 : 5 but have the wrong LCM.
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