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Find the least number which when divided by 12, 27 and 35 leaves 6 as a remainder?
- a)3774
- b)3780
- c)3786
- d)4786
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Find the least number which when divided by 12, 27 and 35 leaves 6 as ...
Number = LCM (12, 17, 35) + 6 = 3780 + 6 = 3786
Most Upvoted Answer
Find the least number which when divided by 12, 27 and 35 leaves 6 as ...
To find the least number that satisfies the given conditions, we can use the concept of the least common multiple (LCM). The LCM is the smallest positive integer that is divisible by all the given numbers.
Given:
Numbers to be divided by: 12, 27, and 35
Remainder: 6
To find the LCM, we need to find the prime factorization of each number and then take the highest power of each prime factor.
Prime factorization of 12:
12 = 2^2 * 3^1
Prime factorization of 27:
27 = 3^3
Prime factorization of 35:
35 = 5^1 * 7^1
Taking the highest power of each prime factor, we have:
2^2 * 3^3 * 5^1 * 7^1 = 4 * 27 * 5 * 7 = 3780
Therefore, the least number that satisfies the given conditions and has a remainder of 6 when divided by 12, 27, and 35 is 3780.
Hence, the correct answer is option C) 3780.
Given:
Numbers to be divided by: 12, 27, and 35
Remainder: 6
To find the LCM, we need to find the prime factorization of each number and then take the highest power of each prime factor.
Prime factorization of 12:
12 = 2^2 * 3^1
Prime factorization of 27:
27 = 3^3
Prime factorization of 35:
35 = 5^1 * 7^1
Taking the highest power of each prime factor, we have:
2^2 * 3^3 * 5^1 * 7^1 = 4 * 27 * 5 * 7 = 3780
Therefore, the least number that satisfies the given conditions and has a remainder of 6 when divided by 12, 27, and 35 is 3780.
Hence, the correct answer is option C) 3780.
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Find the least number which when divided by 12, 27 and 35 leaves 6 as a remainder?a)3774b)3780c)3786d)4786e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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