The greatest 4-digit number which when divided by 20, 24 and 45 leaves a remainder of 11 in each case is

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9999

9998

9997

9731

answer is D.

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Detailed Solution

Concept- The least common multiple of two numbers is the smallest number that can be divided by both. It is possible to compute it for two or more integers as well as two or more fractions.
Here, we have the numbers 20, 24 and 45.
Prime factors of

Prime factors of

We know that L.C.M. is the product of each prime factor of highest power.
Thus, L.C.M. of 20,24 and

The greatest four-digit number

.
When dividing 9999 by 360, we get the remainder 279.
So, the greatest four-digit number divisible by 360 is

.
Now, the greatest four-digit number divisible by 360 and leaving a remainder 11 is

Hence, the correct answer is option 4) 9731.

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