## Multiples and factors

Do you draw a blank when you see LCM and GCF? Don’t worry, these acronyms stand for concepts that make sense. They help you find the common denominator of two or more fractions, simplify fractions, and add and subtract fractions.

Let’s get started

Multiple – The product of a given number and a nonzero whole number.

Do you draw a blank when you see LCM and GCF? Don’t worry, these acronyms stand for concepts that make sense. They help you find the common denominator of you or more fractions, simplify fractions, and add and subtract fractions.

Let’s get started

Multiple – The product of a given number and a nonzero whole number.

Multiples of 2 are

2 x 1 = 2, 2 x 2 = 4, 2 x 3 = 6, and so on.

Example Find the first four multiples of 8

Here’s how multiply 8 by the numbers 1 through 4.
8 x 1 = 8, 8 x 2 =16, 8 x 3 = 24, 8 x 4 = 32
So, the first four multiples of 8 are 8, 16, 24, 32.

Sometimes a number is a multiple of two or more numbers. A special common multiple is the least common multiple.

Least Common Multiple (LCM) – The smallest or least, number that is a multiple of two or more given numbers.

Example Fine the least common multiple (LCM) of 2 and 9.

Here’s how

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18
Multiples of 9: 9, 18, 27, 36, 45

So, the LCM of 2 and 9 is 18.

Another important idea is that of factor.

Factor – A number that divides a given number evenly (that is, with remainder of 0).

5 is a factor of 30 because 30 / 5 = 6
So, 6 is also a factor of 30, because 30 / 6 = 5.

Example: Find all the factors of 30.

Here’s how we know 1 is a factor, so 30 is also a factor because 30 / 1 = 30. Then try dividing by 2, 3, 4, and so on, to get the rest of the factors.

30 / 1 = 30
30 / 2 = 15
30 / 3 = 10
30 / 4 = 7 R2   4 is not a factor
30 / 5 = 6
30 / 6 = 5

So, because dividing 30 by 6 gives 5, we have all the factors: 1, 2, 3, 5, 6, 10, 15, 30

A special factor is called the greatest common factor.

Greatest Common Factor (GCF) – The greatest number that divides two or more numbers evenly.

Example What is the greatest common factor (GCF) or 24 and 30?

Here’s How
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

So, the GCF of 24 and 30 is 6.

2 x 1 = 2, 2 x 2 = 4, 2 x 3 = 6, and so on.

Example Find the first four multiples of 8

Here’s how multiply 8 by the numbers 1 through 4.
8 x 1 = 8, 8 x 2 =16, 8 x 3 = 24, 8 x 4 = 32
So, the first four multiples of 8 are 8, 16, 24, 32.

Sometimes a number is a multiple of two or more numbers. A special common multiple is the least common multiple.

Least Common Multiple (LCM) – The smallest or least, number that is a multiple of two or more given numbers.

Example Fine the least common multiple (LCM) of 2 and 9.

Here’s how

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18
Multiples of 9: 9, 18, 27, 36, 45

So, the LCM of 2 and 9 is 18.

Another important idea is that of factor.

Factor – A number that divides a given number evenly (that is, with remaindr of 0).

5 is a factor of 30 because 30 / 5 = 6
So, 6 is also a factor of 30, because 30 / 6 = 5.

Example: Find all the factors of 30.

Here’s how we know 1 is a factor, so 30 is also a factor because 30 / 1 = 30. Then try dividing by 2, 3, 4, and so on, to get the rest of the factors.

30 / 1 = 30
30 / 2 = 15
30 / 3 = 10
30 / 4 = 7 R2   4 is not a factor
30 / 5 = 6
30 / 6 = 5

So, because dividing 30 by 6 gives 5, we have all the factors: 1, 2, 3, 5, 6, 10, 15, 30

A special factor is called the greatest common factor.

Greatest Common Factor (GCF) – The greatest number that divides two or more numbers evenly.

Example What is the greatest common factor (GCF) or 24 and 30?

Here’s How
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

So, the GCF of 24 and 30 is 6.

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