The ratio of the ages of two brothers is 7 : 15. The LCM of their ages is 210. What is the age of the elder brother?
30
30 is correct.
Let the ages be \(7k\) and \(15k\) years. Since 7 and 15 are co-prime, their LCM is \(7\times15\times k = 105k\).
\(105k = 210 \Rightarrow k = 2\).
The ages are \(7\times2=14\) and \(15\times2=30\) years, so the elder brother is 30 years old. Check: LCM of 14 and 30 is 210.
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