Answer:
ABCD=9564 LCM(9,5,6,4)=180
Explanation:
a= Smallest 2 digit number =10
r= Smallest composite number =4
There ABCD when divided by 10,15,21 and 28 leaves remainder 4, 9, 15, 22.
Hence, the number can be written as:
10k_1+4, 15k_2+9, 21k_3+15, 28k_4+22or 10k_1-6, 15k_2-6, 21k_3-6, 28k_4-6
Hence, the required number when divided by LCM of (10,15,21,28) leaves a remainder of -6.
LCM of (10,15,21,28) =420
Largest 4 digit number divisble by 420 is 9660.
Therefore required number is = 9660-6=9654