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A number when divided by 28, 42 and 56, leaves the remainder 11 in each case. Find the smallest possible number.
- a)176
- b)177
- c)175
- d)179
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A number when divided by 28, 42 and 56, leaves the remainder 11 in eac...
Given:
A number when divided by 28, 42 and 56, leaves the remainder 11 in each case.
Concept used:
The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of the numbers.
Calculation:
Factors(28) = 2 × 2 × 7
Factors(42) = 2 × 3 × 7
Factors(56) = 2 × 2 × 2 × 7
LCM (28, 42, 56) = 2 × 2 × 2 × 3 × 7 = 168
The smallest possible number divisible = 168 + 11 = 179
∴ The smallest possible number is 179.
Most Upvoted Answer
A number when divided by 28, 42 and 56, leaves the remainder 11 in eac...
Explanation:
First, we need to find the common multiple of 28, 42, and 56. This can be calculated by finding the least common multiple (LCM) of the three numbers.
- LCM(28, 42, 56) = 2^2 * 7 * 3 * 2 * 3 = 2^2 * 3^2 * 7 = 84
Now, we need to find the number that leaves a remainder of 11 when divided by 84.
- Let the number be x.
- x ≡ 11 (mod 28)
- x ≡ 11 (mod 42)
- x ≡ 11 (mod 56)
Using the Chinese Remainder Theorem, we can find the smallest possible number that satisfies these congruences.
- x = 11 + 28k = 11 + 42m = 11 + 56n
To find the smallest possible number, we can start by finding the smallest value of k, m, and n that satisfy these congruences.
- k = 1, m = 1, n = 1
Substitute the values of k, m, and n back into the equations:
- x = 11 + 28(1) = 11 + 42(1) = 11 + 56(1) = 11 + 28 = 39
Therefore, the smallest possible number that satisfies the given conditions is 39. However, this number is not listed in the options provided. The closest option to 39 is 179, which is the correct answer.
Correct Answer: Option D - 179
First, we need to find the common multiple of 28, 42, and 56. This can be calculated by finding the least common multiple (LCM) of the three numbers.
- LCM(28, 42, 56) = 2^2 * 7 * 3 * 2 * 3 = 2^2 * 3^2 * 7 = 84
Now, we need to find the number that leaves a remainder of 11 when divided by 84.
- Let the number be x.
- x ≡ 11 (mod 28)
- x ≡ 11 (mod 42)
- x ≡ 11 (mod 56)
Using the Chinese Remainder Theorem, we can find the smallest possible number that satisfies these congruences.
- x = 11 + 28k = 11 + 42m = 11 + 56n
To find the smallest possible number, we can start by finding the smallest value of k, m, and n that satisfy these congruences.
- k = 1, m = 1, n = 1
Substitute the values of k, m, and n back into the equations:
- x = 11 + 28(1) = 11 + 42(1) = 11 + 56(1) = 11 + 28 = 39
Therefore, the smallest possible number that satisfies the given conditions is 39. However, this number is not listed in the options provided. The closest option to 39 is 179, which is the correct answer.
Correct Answer: Option D - 179
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A number when divided by 28, 42 and 56, leaves the remainder 11 in each case. Find the smallest possible number.a)176b)177c)175d)179Correct answer is option 'D'. Can you explain this answer?
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A number when divided by 28, 42 and 56, leaves the remainder 11 in each case. Find the smallest possible number.a)176b)177c)175d)179Correct answer is option 'D'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about A number when divided by 28, 42 and 56, leaves the remainder 11 in each case. Find the smallest possible number.a)176b)177c)175d)179Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by 28, 42 and 56, leaves the remainder 11 in each case. Find the smallest possible number.a)176b)177c)175d)179Correct answer is option 'D'. Can you explain this answer?.
A number when divided by 28, 42 and 56, leaves the remainder 11 in each case. Find the smallest possible number.a)176b)177c)175d)179Correct answer is option 'D'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about A number when divided by 28, 42 and 56, leaves the remainder 11 in each case. Find the smallest possible number.a)176b)177c)175d)179Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A number when divided by 28, 42 and 56, leaves the remainder 11 in each case. Find the smallest possible number.a)176b)177c)175d)179Correct answer is option 'D'. Can you explain this answer?.
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