Latest TCS Aptitude Question SOLUTION: Which of the following represents the largest 4 digit number which can be added to 7855 in order to make the derived number divisible by each of the following numbers 12,14,21,33 a

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Which of the following represents the largest 4 digit number which can be added to 7855 in order to make the derived number divisible by each of the following numbers 12,14,21,33 and 54?

Asked In TCS Ggopinath (4 years ago)

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Anushka  (4 years ago)

12(2*2*3),14(2*7),21(3*7),33(3*11),54(2*3*3*3)
LCM OF 12,14,21,33,54 IS=2 x 2 x 3 x 3 x 3 x 7 x 11 = 8316.
So, 8316 - 7855 = 461 is the number you have to add to 7355 so that it is divisible by these 5 numbers.

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Geetha  (4 years ago)

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.

Ans: "B"

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Nazish  (4 years ago)

LCM of 5 no= 8316
so largest 4 digit number to be added is: 2*8316- 7855= 8777 (Ans)

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