MaximizingLCM | Topcoder Archive

Problem Statement

Suppose we have to select exactly N positive integers, each between 1 and M, inclusive. (The integers do not have to be distinct.)

Determine and return the largest possible value of the least common multiple of these integers.

Definition

Class:: MaximizingLCM
Method:: maximize
Parameters:: int, long
Returns:: long
Method signature:: long maximize(int N, long M)
(be sure your method is public)

Notes

The last constraint implies that the answer for any valid test case won't exceed 10^18.

Constraints

N will be between 1 and 50, inclusive.
M will be positive.
M to the power of N will not exceed 10^18.

Examples

```
6
```
```
3
```
```
Returns: 6
```
One optimal solution is to select the numbers 1, 1, 1, 2, 2, 3. Their least common multiple is 6, which is clearly the best possible answer.
```
10
```
```
10
```
```
Returns: 2520
```
Here, the answer is clearly equal to lcm(1,2,3,4,5,6,7,8,9,10).
```
3
```
```
47
```
```
Returns: 97290
```
```
4
```
```
62
```
```
Returns: 12718866
```

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