CAT 2023 Number System Question (Hard)

Question

Let be the least positive integer such that 168 is a factor of . If is the least positive integer such that is a factor of , then equals

Accepted Answer

Given 1. smallest positive integer such that 2. smallest positive integer such that 3. Find --- Step 1 Prime Factorizations Factorize 168 and 1134 into primes. 168 168 2 3 times 3 times 7 1134 1134 div 2 567 567 3 4 times 7 implies 1134 2 times 3 4 times 7 --- Step 2 Find Smallest such that Compute

CAT 2023

Quantitative

Number System

Hard

Let $n$ be the least positive integer such that 168 is a factor of $1134^n$ . If $m$ is the least positive integer such that $1134^n$ is a factor of $168^m$ , then $m+n$ equals

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