# 6 Mathematical terms

It is important to know the meaning of the following terms:

multiples

lowest common multiple

factors

common factors

prime numbers

## Multiples

A multiple of a number can be found by multiplying that number by any whole number e.g. multiples of 2 include 2, 4, 6, 8, 10 etc. (all are in the 2 times table).

**Note**: To check if a number is a multiple of another, see if it divides exactly into the multiple, e.g. to see if 3 is a multiple of 81 do 81 ÷ 3 = 27. It divides exactly so 81 *is*a multiple of 3.

## Lowest common multiple

In maths, we sometimes need to find the lowest common multiple of numbers.

The lowest common multiple (LCM) is simply the smallest multiple that is common to more than one number.

### Example: Lowest common multiple of 3 and 5

Hint: when looking for multiples, it is easiest to start by listing the multiples of the highest number first. This saves you going any further than you need to with the list.

The first few multiples of 5 are:

5, 10,

**15**, 20, 25, 30 etc.

The first few multiples of 3 are:

3, 6, 9, 12,

**15**, 18, 21 etc.

You can see that the lowest number that is a common multiple of 3 and 5 is 15.

### Activity 12: Finding the lowest common multiple

Find the lowest common multiple of:

6 and 12

2 and 7

#### Answer

The lowest common multiple of 6 and 12 is 12:

Multiples of 12:

**12**, 24, 36, 48, 60 etc.Multiples of 6:

6,

**12**, 18, 24, 30 etc.You can see from the list that 24 is also a common multiple of 6 and 12, but 12 is the lowest common multiple.

The lowest common multiple of 2 and 7 is 14:

Multiples of 7:

7,

**14**, 21, 28, 35, 42 etc.Multiples of 2:

2, 4, 6, 8, 10, 12,

**14**etc.

## Factors, common factors and prime numbers

Factors of a number divide into it exactly. Factors of all numbers include 1 and the number itself. However, most numbers have other factors as well. If you think of all of the numbers that multiply together to make that number, you will find all of the factors of that number.

### Example: What are the factors of 8?

8 × 1 = 8

2 × 4 = 8

So the factors of 8 are 1, 2, 4 and 8.

### Activity 13: Finding factors

What are the factors of 54?

What are the factors of 165?

#### Answer

The factors of 54 are 1, 2, 3, 6, 9, 18, 27 and 54

The factors of 165 are 1, 3, 5, 11, 15, 33, 55 and 165

A common factor is a factor that goes into more than one number. For example, 4 is a common factor of 8 and 12 because it divides exactly into both numbers.

**Prime Numbers**

A prime number is a number which only has 2 factors: 1 and itself.

The prime numbers between 1 and 20 are 2, 3, 5, 7, 11, 13, 17 and 19.

**Note**:

1 is

*not*a prime number as it only has one factor.- 2 is the only even prime number.

You have now learned how to use all four operations, how to work with negative numbers and learned some important mathematical terms. Every other mathematical concept hinges around what you have learned so far; so once you are confident with these, you’ll be a success!

## Summary

In this section you have:

learned some key mathematical terms: multiple, lowest common multiple, factor, common factor and prime number

identified the lowest common multiple

identified factors.