Highest Common Factor and Lowest Common Multiple Worksheet

In this activity, you will need to be able to find a common denominator and reduce a fraction in order to solve a range of questions.

Finding a common denominator

The lowest common denominator is the smallest number that is exactly divisible by each denominator of a set of fractions.

Sometimes when we have to add two fractions, we cannot do it because the denominators are different, both the denominators need to be the same.

To find the lowest common denominator, we see if the larger denominator (20) can be divided by the smaller denominator (4).

20 ÷ 4 = 5.

Therefore we multiply the top and bottom of by 5.

This equals

Reducing a Fraction

We can reduce this fraction and make it simpler by dividing the top and the bottom of the fraction by the same number.

We want to reduce a fraction to its lowest terms so we divide the top and the bottom number by their highest common factor.

The highest number that goes into 8 and 20 is 4.

8 ÷ 4 = 2

20 ÷ 4 = 5

Therefore

Over to you now to use this knowledge to solve a range of different questions.

When we work out the following calculation, what is the lowest common denominator we should choose for both fractions?

When we work out the following calculation, what is the lowest common denominator we should choose for both fractions and what is the final answer?

Reduce the fraction below to its lowest terms;

(Write your answer as a fraction using the / sign e.g. 4/5, don't leave any spaces.)

Reduce this fraction to its lowest terms;

Choose the correct answer from the options given below.

2/4

2/5

1/5

1/6

Reduce this fraction to its lowest terms;

Write your answer as a fraction using the / sign e.g. 7/8 - don't leave any spaces.

in its simplest form is

Correct

Incorrect

Choose the fractions that can be reduced to in its simplest form...

	4/6	5/6	6/9	20/30
Can be reduced to 2/3 in its simplest form

Two explorers have gone to a treasure island to search for treasure chests, full of gold coins.

They know that there are the same number of gold coins on each island.

But the chests contain 8 gold coins on one island and 36 gold coins on the other island.

What is the minimum number of gold coins they will find on each island?

Treasure chest

A parrot squawks every 12 seconds.

A toad croaks every 9 seconds.

They both make a noise at the same time.

When will they next make a noise at the same time?

ANSWERS

Question 1

When we work out the following calculation, what is the lowest common denominator we should choose for both fractions?

CORRECT ANSWER

6

EDDIE SAYS

How did you get on? We had to find the lowest common multiple of 2 and 3, which is 6.

ANSWERS

Question 2

When we work out the following calculation, what is the lowest common denominator we should choose for both fractions?

CORRECT ANSWER

12

EDDIE SAYS

Again, we had to find the lowest common multiple of 4 and 3, which is 12.

ANSWERS

Question 3

When we work out the following calculation, what is the lowest common denominator we should choose for both fractions and what is the final answer?

CORRECT ANSWER

EDDIE SAYS

This time, we had to first find the lowest common multiple of 5 and 10, which is 10 because 10 divided by 5 = 2. Then to complete the calculation we did: 4/10 + 3/10 = 7/10 This is a little tricky but stick with it! Soon the process will come naturally to you.

ANSWERS

Question 4

Reduce the fraction below to its lowest terms;

(Write your answer as a fraction using the / sign e.g. 4/5, don't leave any spaces.)

CORRECT ANSWER

1/3
1 / 3

EDDIE SAYS

The highest common factor of 6 and 18 is 6. 6 ÷ 6 = 1 18 ÷ 6 = 3 This leaves us with the fraction 1/3.

ANSWERS

Question 5

Reduce this fraction to its lowest terms;

Choose the correct answer from the options given below.

CORRECT ANSWER

2/5

EDDIE SAYS

The highest common factor of 12 and 30 is 6. 12 ÷ 6 = 2 30 ÷ 6 = 5 This leaves us with the fraction 2/5. You’re making great progress!

ANSWERS

Question 6

Reduce this fraction to its lowest terms;

Write your answer as a fraction using the / sign e.g. 7/8 - don't leave any spaces.

CORRECT ANSWER

7/8
7 / 8

EDDIE SAYS

The highest common factor of 49 and 56 is 7. 49 ÷ 7 = 7 56 ÷ 7 = 8 This leaves us with the fraction 7/8.

ANSWERS

Question 7

in its simplest form is

CORRECT ANSWER

Incorrect

EDDIE SAYS

"2/3 in its simplest form is 1/1.5" is an incorrect statement because a fraction cannot have a decimal numerator, as it's already part of a whole one.

ANSWERS

Question 8

Choose the fractions that can be reduced to in its simplest form...

CORRECT ANSWER

	4/6	5/6	6/9	20/30
Can be reduced to 2/3 in its simplest form

EDDIE SAYS

We need to carefully check each answer in this question. 4/6, 6/9 and 20/30 can all be reduced to 2/3 in their simplest form.

ANSWERS

Question 9

Two explorers have gone to a treasure island to search for treasure chests, full of gold coins.

They know that there are the same number of gold coins on each island.

But the chests contain 8 gold coins on one island and 36 gold coins on the other island.

What is the minimum number of gold coins they will find on each island?

Treasure chest

CORRECT ANSWER

72

EDDIE SAYS

On one island, the explorer will find the coins in chests of 8 and on the other island, the explorer will find the coins in chests of 36. This question requires us to find the lowest common multiples of 8 and 36. The lowest common multiple of 8 and 36 is 72. Therefore, the explorers will find at least 72 coins on each island.

ANSWERS

Question 10

A parrot squawks every 12 seconds.

A toad croaks every 9 seconds.

They both make a noise at the same time.

When will they next make a noise at the same time?

CORRECT ANSWER

EDDIE SAYS

This question requires us to find the lowest common multiple. The lowest common multiple of 9 and 12 is 36. The parrot and toad will both make a noise at the same time after 36 seconds! Great focus, that’s another activity completed.