Question

What is number when divided by 10 leaves remainder 9 and when divided by 9 leaves remainder 8 and when divided by 7 leaves remainder 6 so on till 1

Answer 1

Since the remainders and divisors differ by '1' in each case:
Find the lcm of (10-1), (9-1), (8-1),...(2-1)
It just means to find the lcm of 9,8,7,6,5,4,3,2,1
9=3^2.... 8=2^3...7=7...6=2*3.....5=5....4=2^2....3=3...2=2..1==1
Hence LCM = 3^2 * 2^3 * 7 * 5 = 2520
Hence the required number = 2520 - 1 = 2519
Hence 2519 when divided by 10 leaves a remainder 9, when divided by 9 leaves remainder 8, when divided by 8 leaves remainder 7 and so on...
Hope it helps

Answer 2

359 is the required Anwer of question