Multiples

Background

There are times when we have two numbers, say like 4 and 6, and we need to find numbers that both 4 and 6 are a factor of. Those numbers are called multiples.

Question

What are some multiples of 4? 6? Which are common? What is the lowest common multiple of 4 and 6?

Answer

4: 4, 8, 12, 16, 20, 24

6: 6, 12, 18, 24, 30 

12 and 24 are common. Any multiple of 12 will be common to both 4 and 6.

12 is the lowest common multiple of 4 and 6 

 Analysis

We explored the concept of factors in Factors and Factoring, where we took a composite number, say like 12, and found its factors (1, 2, 3, 4, 6, 12).

We can go the other way and start with a number and multiply it by other numbers to find multiples.

For instance, if we have the number 4, we can find some of it's multiples:

4 x 1 = 4
4 x 2 = 8
4 x 3 = 12
4 x 4 = 16
4 x 5 = 20
4 x 6 = 24

4, 8, 12, 16, 20, and 24 are a few of the multiples of 4.

We can do the same with 6:

6 x 1 = 6
6 x 2 = 12
6 x 3 = 18
6 x 4 = 24
6 x 5 = 30

6, 12, 18, 24, and 30 are a few of the multiples of 6.

We can look at which of the multiples of 4 and 6 are common. 12 and 24 in this list are common, and if we were to continue looking for more common multiples, all the multiples of 12 would be common to both 4 and 6:

12 x 1 = 12 = 4 x 3 = 6 x 2
12 x 2 = 24 = 4 x 6 = 6 x 4
12 x 3 = 36 = 4 x 8 = 6 x 6
12 x 4 = 48 = 4 x 12 = 6 x 8

and so on.

Vocabulary used:

• Factor - a natural number that multiplied by another natural number results in a product. For instance, the factors of 6 are 1, 6 (1 x 6), 2 and 3 (2 x 3).

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Numbers:

• Whole Numbers

Operations:

• Multiplication

Associated Operations

• Factors and Factoring

Where might we go?

Operations with different kinds of numbers:

• Addition, subtraction, and Rational Numbers

Relations:

• Greater/Lesser Than and Rational Numbers
• Equality and Rational Numbers