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Sikta Roy
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Asked: 2024-03-17T00:41:19+05:30 In:

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

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Let n be the least positive integer such that 168 is a factor of 1134n. If m is the least positive integer such that 1134n is a factor of 168m, then m+n equals
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  1. Sikta Roy
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    The prime factorizations of 168 and 1134 are as follows:
    168 = 23 × 3 × 7
    1134 = 2 × 34 × 7
    Clearly, the smallest positive integral value of n, such that 168 is a factor of 1134n is 3.
    1134n = 11343 = 23 × 312 × 73
    Clearly, the smallest positive integral value of m, such that 11343 is a factor of 168m is 12.
    Therefore, m + n = 12 + 3 = 15

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