Question

Find the greatest 4 digit number which when divided by 20, 24 and 45 leaves a remainder 18 in each case.​

Answer 1

Answer:

9738

Step-by-step explanation:

The Chinese Remainder Theorem says that your system of congruences has a unique solution modulo 360 = lcm(20,24,45). Since 18 is clearly that solution, the answer is the greatest 4-digit number of the form 18 + 360n, which is 18+360*27=9738.

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