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The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
- a)10
- b)14
- c)23
- d)30
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The least number which should be added to 2497 so that the sum is exac...
L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 2497 by 60, the remainder is 37.
L.C.M. of 5, 6, 4 and 3 = 60. Number to be added = (60 - 37) = 23.
Most Upvoted Answer
The least number which should be added to 2497 so that the sum is exac...
To find the least number that should be added to 2497 to make it divisible by 5, 6, 4, and 3, we need to find the least common multiple (LCM) of these four numbers.
Finding the LCM involves finding the smallest number that is divisible by all the given numbers.
First, let's find the LCM of 5 and 6:
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
The LCM of 5 and 6 is 30, as it is the smallest number that appears in both lists.
Now, let's find the LCM of 30 and 4:
Multiples of 30: 30, 60, 90, 120, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
The LCM of 30 and 4 is 60, as it is the smallest number that appears in both lists.
Finally, let's find the LCM of 60 and 3:
Multiples of 60: 60, 120, 180, 240, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
The LCM of 60 and 3 is 60, as it is the smallest number that appears in both lists.
Therefore, the LCM of 5, 6, 4, and 3 is 60.
To make 2497 divisible by 60, we need to find the remainder when 2497 is divided by 60 and subtract it from 60.
2497 ÷ 60 = 41 remainder 37
So, we need to add (60 - 37) = 23 to 2497 to make it divisible by 5, 6, 4, and 3.
Hence, the answer is option C) 23.
Finding the LCM involves finding the smallest number that is divisible by all the given numbers.
First, let's find the LCM of 5 and 6:
Multiples of 5: 5, 10, 15, 20, 25, 30, ...
Multiples of 6: 6, 12, 18, 24, 30, ...
The LCM of 5 and 6 is 30, as it is the smallest number that appears in both lists.
Now, let's find the LCM of 30 and 4:
Multiples of 30: 30, 60, 90, 120, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, ...
The LCM of 30 and 4 is 60, as it is the smallest number that appears in both lists.
Finally, let's find the LCM of 60 and 3:
Multiples of 60: 60, 120, 180, 240, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, ...
The LCM of 60 and 3 is 60, as it is the smallest number that appears in both lists.
Therefore, the LCM of 5, 6, 4, and 3 is 60.
To make 2497 divisible by 60, we need to find the remainder when 2497 is divided by 60 and subtract it from 60.
2497 ÷ 60 = 41 remainder 37
So, we need to add (60 - 37) = 23 to 2497 to make it divisible by 5, 6, 4, and 3.
Hence, the answer is option C) 23.
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The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:a)10b)14c)23d)30e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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