Multiples
Multiples of a number are the products you get when multiplying that number by 1, 2, 3, 4, and so on. For example, the multiples of 5 are 5, 10, 15, 20, 25, and onward. A common multiple is a number that appears in the multiple lists of two or more numbers, and the smallest one is the least common multiple (LCM). This concept is covered in Chapter 3 of Saxon Math Course 2 for 7th grade math and is essential for finding common denominators when adding or subtracting fractions with unlike denominators.
Key Concepts
Property The multiples of a number are produced by multiplying the number by 1, by 2, by 3, by 4, and so on. A number appearing in the lists of two different numbers is a common multiple .
Examples The multiples of 5 are: $5, 10, 15, 20, 25, 30, ...$ The multiples of 8 are: $8, 16, 24, 32, 40, 48, ...$ The common multiples of 4 and 6 are $12, 24, 36, ...$ because they appear in both lists.
Explanation Think of multiples as skip counting! To find the multiples of a number, you just keep adding that number to itself. It is like building a ladder where each rung is one more group of that number. A common multiple is a number that shows up in the lists for two different numbers, like a landmark they both pass.
Common Questions
What are multiples of a number?
Multiples are the products of a number and the counting numbers. The multiples of 5 are 5, 10, 15, 20, 25, 30, and so on. Every number has infinitely many multiples, and the smallest multiple of any number is the number itself.
What is a common multiple?
A common multiple is a number that is a multiple of two or more numbers. For example, 24 is a common multiple of 4 and 6 because 4 x 6 = 24 and 6 x 4 = 24. Common multiples of 4 and 6 include 12, 24, 36, 48, and so on.
How do you find the least common multiple?
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... and multiples of 6 are 6, 12, 18... The LCM is 12 because it is the first number in both lists.
Why are multiples important for fractions?
To add or subtract fractions with different denominators, you need a common denominator, which is a common multiple of both denominators. The LCM gives you the smallest possible common denominator, keeping the numbers manageable.
What is the difference between factors and multiples?
Factors divide evenly into a number (factors of 12: 1, 2, 3, 4, 6, 12), while multiples are what you get by multiplying a number by counting numbers (multiples of 12: 12, 24, 36...). Factors are finite; multiples are infinite.
When do students learn about multiples?
Multiples are introduced in elementary school and studied more formally in 7th grade. Saxon Math Course 2 covers multiples and the LCM in Chapter 3, applying them directly to fraction operations with unlike denominators.