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Which of the following represents the largest 4 digit number which can be added 7249 in order to make the derived number divisible by each of 12,14,21,33 and 54. a)9123 b)9383 c)8727 d)none of these

Which of the following represents the largest 4 digit number which can be added 7249 in order to make the derived number divisible by each of 12,14,21,33 and 54.
a)9123       b)9383
c)8727       d)none of these 

Grade:12th pass

5 Answers

kartheeek
24 Points
9 years ago
ans is none of these
l.c.m. of 12,14,21,33,54 is 756
and 756*2=1512 is also divisible by all the numbers
so the ans is 1512+7249=8761
 
Lovesh Sinha
18 Points
9 years ago
LCM is wrong....check it again?
 
kartheeek
24 Points
9 years ago
ans is l.c.m.of 12,14,21,33,54 – 7249=8316-7429 or 8316*2-7429
Miriyla Gowtham
15 Points
5 years ago
THE LCM OF 12,14,21,33,54 IS 8316.
BUT 8316*2 = 16632 IS DIVISIBLE BY ALL ABOVE NUMBERS SO ANS IS 16632 – 7249 = 9383 (ANS)
 
nikhil
13 Points
5 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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