## Saturday, December 27, 2014

### LCMRange

Problem:

 TopCoder Problem Statement - LCMRange Single Round Match 162 Round 1 - Division II, Level One

Overview:

Find the Least Common Multiple of a range of numbers.

Java Source:
```01: public class LCMRange {
02:
03:  public int lcm(int first, int last) {
04:
05:   /*
06:   * The Least Common Multiple must be a multiple of last, so we'll
07:   * start there and increment by last to get the next value.
08:   */
09:   int lcm = last;
10:
11:   boolean found = false;
12:
13:   // Continue until we find the LCM
14:   while (!found)  {
15:
16:    int i = first;
17:
18:    /*
19:    * Check each number between first and last (inclusive) to ensure
20:    * that lcm is a multiple.
21:    */
22:    while (i <= last)  {
23:
24:     // If it doesn't divide evenly, skip this number.
25:     if ((lcm % i) != 0)  {
26:      break;
27:     }
28:
29:     i ++;
30:    }
31:
32:    /*
33:    * If we've tested all the numbers, then we've successfully found
34:    * a Least Common Multiple
35:    */
36:    if (i > last)  {
37:     found = true;
38:
39:    } else  {
40:
41:     /*
42:     * Otherwise try the next number.  We know it must be a
43:     * multiple of first, so we can increment by that amount.
44:     */
45:     lcm += last;
46:    }
47:   }
48:
49:   return lcm;
50:  }
51: }
```
Notes:

The constraints of this problem make it small enough that a brute-force method works well. We could just start at 1 and check to see if it is a Least Common Multiple (LCM) of each number in the range. If not, just increment by 1 and try again. A simple optimization is to note that our answer must be a multiple of last. So we can start our search there, and increment by the value of last to get the next number to test.

The % operator is used to determine if one number divides another evenly. if ((a % b) == 0) then b evenly divides a. Or, a is a multiple of b.

Note the break; statement in the inner-most while loop. This lets us quit on a potential LCM as soon as we find a number that it is not a multiple of. When the break is encountered, i will be <= last, and the if statement below will use this to determine if a LCM has been found or not.