Question

The least number which when divided by 48,64,90,120 leave the remainders 38,54,80,110 respectively is

Answer 1

dividend = divisor * quotient + remainder

dividents = 48, 64,....
quotient = we dont care
divisor = same number (say a)
remainders = 38, 54,...

Answer 2

i did nt get it

Answer 3

let
x = 48*q + 38
(x-38) -> divisible by 48
i.e.,
(x-38+48) -> divisible by 48
i.e., (x+10) -> divisible by 48

we want this number to be divisible by all the divisors.
i.e., (x+10) is the LCM of 48, 64, 90 and 120
x+10 = 2880
\(\boxed{x=2870}\)