Question

the least number which when divided by 42,72 and 84 leaves the remainder 25,55 and 67 respectively is equal to

Answer 1

Required number={LCM(42+25,72+55,84+67)
= LCM of 67,127,151

Answer 2

let A be such number that satisfies above condition

then ,
A = 42k + 25-----------(1)
A = 72Y + 55-----------(2)
A = 84Z + 67------------(3)

From 1 and 2
42k + 25 = 72Y + 55
42k = 72Y +30
7K = 12Y + 5
K = (12Y+ 5)/7
we need to find Y such that we get K as positive integer.(apply Hit and trial method)

possible value of Y is 6

then A = 72(6) + 55
= 487

When we divide 487 by 84 we get 67 as Remainder.

So, 487 is Required No.