Question

find the greatest 5-digit number which is exactly divisible by 14,21,35,42& 63?

Answer 1

Hey

Here is your answer,

Suppose we are given that a number when divided by x, y, and z, leaves a remainder of a, b, and c; then the number will be of the format of
N = LCM(x,y,z)*n + constant

If the remainder is same in all divisions then the value of constant is equals to the given remainder i.e 1 here.

LCM(x,y,z) = 630

So we have the equation

N = 630*n + 1

Largest 5 digit number possible = 99999

Now the value of n will be

n = 99999/630 = 158.72 = 158(because n is integer and N should be less than 99999)

So N = 630*158 + 1 = 99541

Hope it helps you!