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Find the smallest number which when divided by 12, 15 and 18 leaves a remainder of 1 in each case, but is perfectly divisible by 11.
- a)901
- b)1,261
- c)1,441
- d)1,801
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Find the smallest number which when divided by 12, 15 and 18 leaves a...
To find the smallest number that satisfies the given conditions, we need to find the least common multiple (LCM) of 12, 15, and 18, and then check which of the options is divisible by 11.
Finding the LCM of 12, 15, and 18:
1. Prime factorize each number:
- 12 = 2^2 * 3
- 15 = 3 * 5
- 18 = 2 * 3^2
2. Take the highest power of each prime factor:
- 2^2 * 3^2 * 5 = 180
So, the LCM of 12, 15, and 18 is 180.
Now, we need to check which of the given options is divisible by 11:
a) 901: Not divisible by 11
b) 1,261: Not divisible by 11
c) 1,441: Divisible by 11 (as 1 + 4 + 4 + 1 = 10, which is divisible by 11)
d) 1,801: Not divisible by 11
Therefore, the smallest number that satisfies the given conditions is 1,441, which is option C.
Finding the LCM of 12, 15, and 18:
1. Prime factorize each number:
- 12 = 2^2 * 3
- 15 = 3 * 5
- 18 = 2 * 3^2
2. Take the highest power of each prime factor:
- 2^2 * 3^2 * 5 = 180
So, the LCM of 12, 15, and 18 is 180.
Now, we need to check which of the given options is divisible by 11:
a) 901: Not divisible by 11
b) 1,261: Not divisible by 11
c) 1,441: Divisible by 11 (as 1 + 4 + 4 + 1 = 10, which is divisible by 11)
d) 1,801: Not divisible by 11
Therefore, the smallest number that satisfies the given conditions is 1,441, which is option C.
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Community Answer
Find the smallest number which when divided by 12, 15 and 18 leaves a...
Long method
LCM of 12, 15 and 18 = 180
Thus, the required number will be 180 or any multiple of 180 plus 1, that is, 181, 361, 541 and so on.
You will have to divide each of these numbers by 11 to check which one is divisible.
1441 will be the first such number.
This method will of course take a lot of time.
Short method:
Start backsolving from the answer choices.
The correct answer has to be divisible by 11.
Out of the five given options, 1441 is the only one that is divisible by 11, and, hence, it has to be the correct answer.
Hence, the correct option is (c).
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Find the smallest number which when divided by 12, 15 and 18 leaves a remainder of 1 in each case, but is perfectly divisible by 11.a)901b)1,261c)1,441d)1,801Correct answer is option 'C'. Can you explain this answer?
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