Let N be a 5-digit number. When N is divided by 6, 12, 15, 24 it leaves respectively 2, 8, 11, 20 as remainders. What is the <strong>GREATEST</strong> value of N?

Explanation

The difference between the divisors and their respective remainders is constant: 6-2 = 4, 12-8=4, etc. Therefore, N = \text{LCM}(6, 12, 15, 24) \times k - 4 = 120k - 4. The largest 5-digit multiple of 120 is 99960. Thus, N = 99960 - 4 = 99956.

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