What are multiples
Multiples are the products you get when you multiply a given number by the counting numbers 1, 2, 3, 4, 5, and so on — they are essentially the results of skip-counting by that number. In 4th grade math with Saxon Math Intermediate 4, Chapter 6, students learn that the first four multiples of 7 are 7, 14, 21, and 28, and that every number has infinitely many multiples. Understanding multiples is foundational for finding least common multiples (LCM), adding and subtracting fractions with different denominators, and identifying patterns in multiplication tables.
Key Concepts
Property A multiple is a product of a given number and a counting number. The multiples of any counting number are the products we get when we multiply the number by 1, 2, 3, 4, 5, 6, and so on. For example, the first four multiples of 3 are 3, 6, 9, and 12.
Example The first four multiples of 7 are: $7 \times 1 = 7$, $7 \times 2 = 14$, $7 \times 3 = 21$, and $7 \times 4 = 28$. The third multiple of 8 is found by calculating $8 \times 3 = 24$. Twelve is a multiple of 1, 2, 3, 4, 6, and 12 because each of those numbers can be multiplied by another whole number to equal 12.
Explanation Think of multiples as the numbers you land on when you're skip counting. If you start at 7 and keep adding 7, you get 14, 21, 28, and so on—these are all multiples of 7! It’s just a way of showing the results from a number’s multiplication table in a sequence that can go on forever.
Common Questions
What is a multiple in math?
A multiple of a number is the product of that number and any counting number. For example, multiples of 5 are: 5 (5x1), 10 (5x2), 15 (5x3), 20 (5x4), and so on without end.
How do you find the multiples of a number?
Multiply the number by 1, 2, 3, 4, 5, etc. in order. This is the same as skip-counting by that number. The multiples of 3 are: 3, 6, 9, 12, 15, ...
What are the first five multiples of 7?
7, 14, 21, 28, 35. These are the products 7x1, 7x2, 7x3, 7x4, and 7x5.
Is 24 a multiple of 6?
Yes. 24 = 6 x 4, so 24 is in the 6 times table and therefore a multiple of 6. You can also verify that 24 / 6 = 4 with no remainder.
When do 4th graders learn about multiples?
In Saxon Math Intermediate 4, Chapter 6, Lessons 51-60, students learn the definition of multiples and practice listing the multiples of various numbers.
How do multiples relate to the concept of common multiples?
A common multiple is a number that appears in the multiple lists of two different numbers. For example, 12 is in the multiples of both 3 and 4. Finding the least common multiple (LCM) is a key skill for adding fractions in 5th grade.