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Question

# A number which when divided by 10 leaves a remainder of 9, when divided by 9 leaves remainder of 8, and when divided by 8 leaves a remainder of 7, is

A
1539
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B
5139
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C
2519
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D
9413
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Solution

## The correct option is C 2519Since the remainders and divisors differ by 1 in each case:So, we find the LCM of (10−1),(9−1),(8−1),...(2−1)It just means to find the LCM of 9,8,7,6,5,4,3,2,19=32....8=23...7=7...6=2×3.....5=5....4=22....3=3...2=2...1=1Therefore, LCM =32×23×7×5=2520Thus, the required number =2520−1=2519Hence, 2519 is the number 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.

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