The least common multiple (LCM) of two distinct prime numbers is their product.
Understanding Prime Numbers and LCM
Before diving into the answer, let's briefly review some key concepts:
- Prime Numbers: A prime number is a whole number greater than 1 that has only two divisors: 1 and itself. Examples include 2, 3, 5, 7, 11, and so on.
- Least Common Multiple (LCM): The LCM of two or more numbers is the smallest positive number that is a multiple of all the given numbers.
Calculating the LCM of Distinct Primes
The reference states: The LCM of two or more prime numbers is equal to their product. This is because prime numbers, by definition, do not share any common factors other than 1. Therefore, to find the smallest number that is a multiple of both primes, you must simply multiply them together.
Examples:
- Example 1: Find the LCM of 3 and 5.
- 3 and 5 are both prime numbers.
- LCM(3, 5) = 3 * 5 = 15.
- Example 2: Find the LCM of 7 and 11.
- 7 and 11 are both prime numbers.
- LCM(7, 11) = 7 * 11 = 77.
General Formula
Let p and q represent two distinct prime numbers. Then,
LCM(*p*, *q*) = *p* * *q*Key Takeaway
The crucial point is that because prime numbers have no shared factors other than 1, their LCM is always their product.
