 # Highest Common Factor and Lowest Common Multiple

In this worksheet, students will be asked to recap their knowledge of common denominators, reducing fractions and then solving worded problems. Key stage:  KS 2

Curriculum topic:   Number: Fractions, Decimals and Percentages

Curriculum subtopic:   Use Common Factors

Difficulty level:   ### QUESTION 1 of 10

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? 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? 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?  • Question 1

When we work out the following calculation, what is the lowest common denominator we should choose for both fractions? 6
EDDIE SAYS
How did you get on? We had to find the lowest common multiple of 2 and 3, which is 6.
• Question 2

When we work out the following calculation, what is the lowest common denominator we should choose for both fractions? 12
EDDIE SAYS
Again, we had to find the lowest common multiple of 4 and 3, which is 12.
• 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? 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.
• 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.)

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.
• Question 5

Reduce this fraction to its lowest terms; Choose the correct answer from the options given below.

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!
• 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.

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.
• Question 7 in its simplest form is 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.
• Question 8

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
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.
• 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? 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.
• 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?  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.
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