Least common multiple
The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all of them. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly. The LCM is most commonly used to find a common denominator when adding or subtracting fractions with unlike denominators. This concept is a fundamental building block in 7th grade math and is covered in Saxon Math, Course 2, where it connects to operations with fractions and rational numbers.
Key Concepts
Property The least common multiple is the smallest number that is a multiple of two or more numbers. The term least common multiple is often abbreviated LCM .
Examples For 6 and 8, check multiples of 8: $8, 16, 24$. Since 24 is divisible by 6, the LCM of 6 and 8 is 24. For 3, 4, and 6, check multiples of 6: Is 6 divisible by 4? No. Is 12 divisible by 4 and 3? Yes! The LCM is 12. For 8 and 10, check multiples of 10: $10, 20, 30, 40$. Since 40 is divisible by 8, the LCM of 8 and 10 is 40.
Explanation The LCM is the very first number you hit that is on everyone’s “multiples” list. Instead of listing out endless numbers, just check the multiples of the biggest number in your set. See if the other numbers divide into it evenly. It is the ultimate shortcut to finding the first spot where all their paths cross!
Common Questions
What is the least common multiple (LCM)?
The least common multiple (LCM) of two or more numbers is the smallest number that is divisible by all of them. For example, the LCM of 3 and 4 is 12.
How do you find the LCM of two numbers?
List the multiples of each number until you find the smallest one they share. For 4 and 6: multiples of 4 are 4, 8, 12, 16...; multiples of 6 are 6, 12, 18... The LCM is 12. Alternatively, use prime factorization.
How is the LCM used with fractions?
The LCM is used as the least common denominator (LCD) when adding or subtracting fractions with unlike denominators. It’s the smallest denominator that both fractions can be converted to.
What is the difference between LCM and GCF?
The LCM (least common multiple) is the smallest number divisible by both; the GCF (greatest common factor) is the largest number that divides both. LCM is used for adding fractions; GCF is used for simplifying fractions.
What is the LCM of 8 and 12?
The LCM of 8 and 12 is 24. Multiples of 8: 8, 16, 24... Multiples of 12: 12, 24... The first common multiple is 24.
When do students learn about LCM?
The least common multiple is typically taught in 6th and 7th grade math as part of number theory and operations with fractions.
Which textbook covers least common multiple?
Saxon Math, Course 2 covers the least common multiple (LCM).