Question

find the greatest four digit no. which when divided by 20, 24 and 45 leaves a remainder of 18 in each case.

Answer 1

Given numbers,
20 , 24 and 45
Prime factorization of
20=2²×5

24=2³×3

45=3²×5

LCM=product of each prime factor of highest power
LCM=2³×3²×5=360

Greatest four digit number=9999
greatest four digit number divisible by all given numbers=9999-remainder when 9999 is divided by LCM of given numbers
greatest four digit number divisible by given numbers=9999-279=9720
Given that,
required number when divided by 20 , 24, 45 leaves remainder 18.
Therefore,required number=9720+18=9738

Hence greatest four digit number when divided by 20,24 and 45 is 9738