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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
- a)12
- b)9
- c)15
- d)24
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Let n be the least positive integer such that 168 is a factor of 1134n...
Explanation:
Finding n:
- We know that 168 = 2^3 * 3 * 7
- To find the least positive integer n such that 168 is a factor of 1134n, we need to divide 1134 by 168
- 1134/168 = 6.75, which is not a whole number
- So, we keep increasing n until we get a whole number
- By trial and error, we find that n = 7 makes 168 a factor of 1134n
Finding m:
- We know that 1134n = 1134*7 = 7938
- To find the least positive integer m such that 1134n is a factor of 168m, we need to divide 168 by 7938
- 168/7938 = 0.0212, which is not a whole number
- Again, we keep increasing m until we get a whole number
- By trial and error, we find that m = 15 makes 1134n a factor of 168m
Calculating m + n:
- m + n = 15 + 7 = 22
Therefore, the correct answer is not listed in the options given.
Finding n:
- We know that 168 = 2^3 * 3 * 7
- To find the least positive integer n such that 168 is a factor of 1134n, we need to divide 1134 by 168
- 1134/168 = 6.75, which is not a whole number
- So, we keep increasing n until we get a whole number
- By trial and error, we find that n = 7 makes 168 a factor of 1134n
Finding m:
- We know that 1134n = 1134*7 = 7938
- To find the least positive integer m such that 1134n is a factor of 168m, we need to divide 168 by 7938
- 168/7938 = 0.0212, which is not a whole number
- Again, we keep increasing m until we get a whole number
- By trial and error, we find that m = 15 makes 1134n a factor of 168m
Calculating m + n:
- m + n = 15 + 7 = 22
Therefore, the correct answer is not listed in the options given.
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Community Answer
Let n be the least positive integer such that 168 is a factor of 1134n...
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
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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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 equalsa)12b)9c)15d)24Correct answer is option 'C'. Can you explain this answer?
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