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Find the largest 4-digit number which when divided by 16, 20, 25 and 48, leaves the same remainder 15 in each case.

Find the largest 4-digit number which when divided by 16, 20, 25 and 48, leaves the same remainder 15 in each case. Correct Answer 9615

LCM of 16, 20, 25 and 48 is 1200. The largest 4-digit number is 9999. On dividing it by 1200, we get 399 as remainder. The largest 4-digit which is divisible by 16, 20, 25 and 48 is 9999-399 = 9600. Therefore, the required number is 9600+15 = 9615.

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