Question

There is a number greater than 1 which when divided by 4, 5 and 6 leaves the same remainder of 3 in each case. Find the largest number, smaller than 1000 which satisfy the given condition.
A) 957
B) 993
C) 960
D) 963

Answer 1

D) 963 is the number that gives a remainder 3 when divided by 4, 5 and 6

Answer 2

Answer:

963

Step-by-step explanation:

Given : There is a number greater than 1 which when divided by 4, 5 and 6 leaves the same remainder of 3 in each case.

To Find:  Find the largest number, smaller than 1000 which satisfy the given condition.

Solution:

First Find the LCM of 4 ,5 and 6

2  | 4,5,6

2  | 2,5,3

3  | 1,5,3

5  | 1,5,1

 | 1,1,1

LCM = $2 \times 2 \times 3 \times 5 = 60$

Now divide 1000 by 60

On dividing we get 40 as remainder .

Now, The required number = $1000-40+3$

                                             = $963$

Hence the number is 963 .

Thus option D is correct.