In this article, we will explore the concept of the smallest shared factor, also known as the lowest common multiple. Our focus is to provide elementary school students with a comprehensive understanding of this mathematical area. We have included practice questions to help them master the topic quickly!

Table of Contents

## Understanding Multiples in Mathematics

A multiple is a number that can be divided evenly, leaving no remainder. It is often helpful for children to think of multiples as numbers found in another number’s multiplication table. For example, 24 is a multiple of 12, as well as 1, 2, 3, 4, 6, 8, and 24. Similarly, the first five multiples of 6 are 6, 12, 18, 24, and 30. It’s important to note that multiples and factors are interconnected. For instance, 4 is a factor of 12, and 12 is a multiple of 4.

## Understanding Common Multiples in Mathematics

A common multiple refers to a number that is divisible by two or more given numbers. Let’s take the numbers 6 and 4 as an example. The number 12 is a common multiple of 6 and 4 because it appears in both the 6 and 4 times tables. Likewise, the common multiples of 6 and 9 are 18, 36, and 54.

## Introducing the Lowest Common Multiple

The lowest common multiple, also known as the least common multiple (LCM), refers to the smallest multiple shared by two or more numbers. Let’s consider the numbers 4 and 6. The common multiples of 4 and 6 are 12, 24, and 36. However, the smallest among these multiples is 12. Thus, the lowest common multiple of 4 and 6 is 12.

## Finding the Lowest Common Multiple

To help children find the lowest common multiple, one effective approach is to encourage them to list the multiples of each number until they identify the first common multiple. Let’s take the numbers 5 and 7 as an example. The LCM of 5 and 7 is 35:

## Learning about the Lowest Common Multiple at Different Grade Levels

Children are first introduced to multiples in kindergarten, even though they might not be familiar with the term. In kindergarten, they may learn to count in multiples of twos, fives, and tens as part of their number bonds and skip-counting lessons. In 1st grade, students begin subtracting multiples of 10 between the range of 10-90 from other multiples of 10 within the same range.

By 2nd grade, children are expected to count within 1000 and skip-count by 5s, 10s, and 100s. In 3rd grade, students learn to multiply by multiples of 10 and delve into the terms “multiple” and “factor” while studying their multiplication facts. In 4th grade, students should be able to identify all factor pairs for whole numbers between 1 and 100. They should also be proficient in recognizing multiples and solving problems involving multiplication and division, applying their knowledge of multiples.

Common multiples are not introduced until 5th grade. At this stage, students are expected to utilize common multiples to express fractions in the same denominators and solve problems involving unequal sharing and grouping, utilizing their knowledge of fractions and multiples.

## The Relevance of Lowest Common Multiples in Math

Lowest common multiples play a crucial role when expressing fractions in the same denominator. This is necessary when adding or subtracting, ordering, or comparing fractions. For example, to calculate 3/5 + 1/6, we need to find the common denominator by determining the lowest common multiple of 5 and 6, which is 30. Consequently, we can convert the fractions to 18/30 + 5/30, resulting in 23/30.

If you’re interested in learning more about other key math vocabulary to help children, check out our Math Dictionary for Kids or explore these math terms:

- What Is Long Multiplication: Explained For Teachers, Parents, and Kids
- What Is A Cube Number: Explained For Teachers, Parents, and Kids
- What Is A Square Number: Explained For Teachers, Parents, and Kids
- What Is The Highest Common Factor: Explained For Teachers, Parents, and Kids

## Practice Questions for Finding the Lowest Common Multiple

- What is the lowest common multiple of 8 and 10?
- Write down all the common multiples of 3 and 8 that are less than 50.
- What is the lowest common multiple of 100 and 50?
- Write down all the common multiples of 4 and 6 that are less than 60.
- What is the lowest common multiple of 1000 and 650?