Question:
(1134)n is divisible by 168. (168)m is divisible by (1134)n. Find the minimum value of n + m
(1134)n is divisible by 168. (168)m is divisible by (1134)n. Find the minimum value of n + m
Updated On: Jan 12, 2026
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Solution and Explanation
The following are the prime factorizations of 1134 and 168:
\(168 = 2^3 × 3 × 7\)
1134 is equal to \(2 × 3^4 × 7. \)
Evidently, three is the least positive integral number of n that allows 168 to be a factor of 1134n.
\(1134^3 = 2^3 × 3^{12} × 7^3 = 1134^n \)
It is evident that 12 is the least positive integral value of m that allows \(1134^3\) to be a factor of 168m.
It follows that \(m + n = 12 + 3 = 15\)
The correct answer is 15.
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