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The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
- a)1008
- b)1015
- c)1022
- d)1032
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The smallest number which when diminished by 7, is divisible 12, 16, 1...
Required Number = (L.C.M of 12, 16, 18,21,28)+7
= 1008 + 7
= 1015
Most Upvoted Answer
The smallest number which when diminished by 7, is divisible 12, 16, 1...
To find the smallest number that satisfies the given conditions, we need to find the least common multiple (LCM) of the given numbers.
Finding the LCM:
Step 1: List out the prime factors of each number.
12 = 2^2 * 3
16 = 2^4
18 = 2 * 3^2
21 = 3 * 7
28 = 2^2 * 7
Step 2: Take the highest power of each prime factor that appears in any of the numbers.
2^4 * 3^2 * 7 = 16 * 9 * 7 = 1008
So, the LCM of 12, 16, 18, 21, and 28 is 1008.
Finding the smallest number:
Let x be the smallest number.
According to the given conditions, x - 7 should be divisible by 1008.
Therefore, x - 7 = 1008k, where k is an integer.
To find the smallest value of x, we need to find the smallest value of k.
If we take the smallest value of k as 1, then x - 7 = 1008 * 1.
Simplifying the equation, we get x = 1008 + 7 = 1015.
Therefore, the smallest number that satisfies the given conditions is 1015.
Hence, the correct answer is option B) 1015.
Finding the LCM:
Step 1: List out the prime factors of each number.
12 = 2^2 * 3
16 = 2^4
18 = 2 * 3^2
21 = 3 * 7
28 = 2^2 * 7
Step 2: Take the highest power of each prime factor that appears in any of the numbers.
2^4 * 3^2 * 7 = 16 * 9 * 7 = 1008
So, the LCM of 12, 16, 18, 21, and 28 is 1008.
Finding the smallest number:
Let x be the smallest number.
According to the given conditions, x - 7 should be divisible by 1008.
Therefore, x - 7 = 1008k, where k is an integer.
To find the smallest value of x, we need to find the smallest value of k.
If we take the smallest value of k as 1, then x - 7 = 1008 * 1.
Simplifying the equation, we get x = 1008 + 7 = 1015.
Therefore, the smallest number that satisfies the given conditions is 1015.
Hence, the correct answer is option B) 1015.
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The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:a)1008b)1015c)1022d)1032Correct answer is option 'B'. Can you explain this answer?
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The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:a)1008b)1015c)1022d)1032Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:a)1008b)1015c)1022d)1032Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:a)1008b)1015c)1022d)1032Correct answer is option 'B'. Can you explain this answer?.
The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:a)1008b)1015c)1022d)1032Correct answer is option 'B'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:a)1008b)1015c)1022d)1032Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:a)1008b)1015c)1022d)1032Correct answer is option 'B'. Can you explain this answer?.
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