Least common multiple

Definition

The least common multiple (LCM) of two or more integers is the smallest positive integer that is divisible by all of them. It is used to find a common denominator in adding or subtracting fractions and in solving problems involving multiples.

5 Must Know Facts For Your Next Test

1. The LCM of two numbers can be found using their prime factorizations.
2. LCM is useful for finding equivalent fractions with a common denominator.
3. The LCM of any number and one is the number itself.
4. For two prime numbers, the LCM is simply their product.
5. The relationship between LCM and GCD (Greatest Common Divisor) can be expressed as: LCM(a, b) * GCD(a, b) = a * b.

Review Questions

• What is the least common multiple of 12 and 15?
• How do you find the LCM using prime factorization?
• Explain how the LCM of two numbers relates to their GCD.

Related terms

Prime Factorization: Breaking down a composite number into its prime factors.

Greatest Common Divisor (GCD): The largest positive integer that divides each of the given integers without leaving a remainder.

Multiple: A product of a number and an integer.