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Chinese Remainder Theorem.

So, 3*5 = 15
15 divided by 2 equals 1 So, the number 15 meets our criteria of being divisible by 2.

Second, we’ll deal with the number 3. We’ll multiply the other digits 2 * 5 = 10.
10 divided by 3 = 1. We are looking for a remainder of 2, so this is not what we want, so let’s continue.
Let’s get the next multiple of 10, which is 20.
20 / 3 = 2
So now we know that the number 20, meets our criteria for dividing this number by three.

Finally we’ll deal with the number 5. Multiplying the other numbers 2 * 3 = 6.
6 / 5 leaves a remainder of 1. We are looking for a remainder of 3, so we'll get the next multiple: 12.
12 / 5 leaves a remainder of 2. Still not what we want. Next multiple=18.
18 / 5 leaves a remainder of 3, which satisfies our criteria.

So, now we have three numbers that satisfy the criteria for each of these numbers. These numbers are 15, 20 and 18. If we add these numbers together (15+20+18) we get the number 53.
You might notice something intersting about this number:
53 divided by 2 leaves a remainder of 1
53 divided by 3 leaves a remainder of 2
53 divided by 5 leaved a remainder of 3

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