Latest Others Aptitude Question SOLUTION: The largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12,14,21,33 and 54 will be?

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(#M40019346) OTHERS Logical Reasoning question Keep an EYE

The largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12,14,21,33 and 54 will be?

Asked In Others mohan lal garg (10 years ago)

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Ranvir Rana  (10 years ago)

answer is 9383
Find the LCM of the given numbers.
12= 2*2*3
14= 2*7
21= 3*7
33= 3*11
54= 3*2*3*3

Max powers of all prime numbers:
2=2
3=3
7=1
11=1

LCM=2^2*3^3*7^1*11^1=8316

8316-7249=1067. Thus, if we add 1067 to 7249, the number will be divisible by all the given numbers.
However, 1067 is not the GREATEST 4-digit number to satisfy the condition.

Next number that will be divisible is:
1067+8316=9383

Thus, adding 9383 to 7249 will give us a number that will be divisible by all the given numbers PLUS 9383 is the greatest 4-digit number that satisfies this condition.

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