Find the greatest five digit number .which is exactly divisible by 14,21,35,42and63.
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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
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
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