The Least Common Multiple (LCM) of two consecutive prime numbers is their product.
Here's why:
Prime numbers are numbers greater than 1 that have only two factors: 1 and themselves. Consecutive prime numbers are prime numbers that follow each other in sequence (e.g., 3 and 5, 11 and 13). By definition, consecutive prime numbers share no common factors other than 1.
The LCM of two numbers is the smallest number that is a multiple of both. Since consecutive prime numbers don't share any factors other than 1, to find a common multiple, you must multiply them together. This product will be the least such multiple.
Example:
- Consider the consecutive prime numbers 7 and 11.
- The multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84,...
- The multiples of 11 are: 11, 22, 33, 44, 55, 66, 77, 88,...
- The least common multiple of 7 and 11 is 77 (7 x 11).
General Rule:
For any two consecutive prime numbers, p and q, where p < q, the LCM(p, q) = p * q.
