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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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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
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The smallest number which when diminished by 7, is divisible 12, 16, 1...
The question asks for the smallest number that satisfies the given conditions: when the number is diminished by 7, it should be divisible by 12, 16, 18, 21, and 28.
To find this number, we can start by finding the least common multiple (LCM) of the given numbers (12, 16, 18, 21, and 28). The LCM is the smallest number that is divisible by all the given numbers.
Finding the LCM of 12, 16, 18, 21, and 28:
1. Prime factorize each number:
- 12 = 2^2 * 3
- 16 = 2^4
- 18 = 2 * 3^2
- 21 = 3 * 7
- 28 = 2^2 * 7
2. Take the highest power of each prime factor:
- 2^4
- 3^2
- 7
3. Multiply these values together to get the LCM:
LCM = 2^4 * 3^2 * 7 = 16 * 9 * 7 = 1008
Now, we know that the smallest number that is divisible by 12, 16, 18, 21, and 28 is 1008.
To find the number that, when diminished by 7, is divisible by these numbers, we need to add 7 to the LCM.
1008 + 7 = 1015
Therefore, the smallest number that satisfies the given conditions is 1015, which is option 'B' in the answer choices.
To find this number, we can start by finding the least common multiple (LCM) of the given numbers (12, 16, 18, 21, and 28). The LCM is the smallest number that is divisible by all the given numbers.
Finding the LCM of 12, 16, 18, 21, and 28:
1. Prime factorize each number:
- 12 = 2^2 * 3
- 16 = 2^4
- 18 = 2 * 3^2
- 21 = 3 * 7
- 28 = 2^2 * 7
2. Take the highest power of each prime factor:
- 2^4
- 3^2
- 7
3. Multiply these values together to get the LCM:
LCM = 2^4 * 3^2 * 7 = 16 * 9 * 7 = 1008
Now, we know that the smallest number that is divisible by 12, 16, 18, 21, and 28 is 1008.
To find the number that, when diminished by 7, is divisible by these numbers, we need to add 7 to the LCM.
1008 + 7 = 1015
Therefore, the smallest number that satisfies the given conditions is 1015, which is option 'B' in the answer choices.
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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)1032Correct answer is option 'B'. Can you explain this answer?
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