The idea in brief. A multiple of a number is what you land on counting on in that number, so the number divides it exactly with nothing left over. To find what two numbers share, write both lists and read across; the first number on both is the first common multiple, and it is not always the two numbers multiplied together.
Lesson video, with the working
Common multiples
3 min 43 s
The film teaches 2 questions in turn. Each question shows first; its working is written as the film explains it.
Question 1 of 12 · Basic · free to tryFind the 6th multiple of 8.Find the 6th multiple of 8.
Find the 6th multiple of 8.
Show the working and the answer
Working
6 × 8 = 48
The 6th multiple of 8 is 48.
Answer: 48
Question 11 of 12 · Challenge · free to tryA number is a multiple of 6 and also a multiple of 8. It is greater than 100…A number is a multiple of 6 and…
A number is a multiple of 6 and also a multiple of 8. It is greater than 100 and less than 130. Find the number.
Common multiples of 6 and 8: 24, 48, 72, 96, (120), 144, ...
5 × 24 = 120
The number is 120.
Answer: 120
For parents
How can I explain P4 common multiples to my child?
Your child identifies multiples of a given 1-digit number and finds common multiples of two given 1-digit numbers.
What your child learns here
Your child identifies multiples of a given 1-digit number and finds common multiples of two given 1-digit numbers. These are explicit MOE Primary 4 outcomes. A multiple comes from multiplying by a whole number; listing the positive multiples in order makes shared values visible and supports questions with a size limit.
Generate successive positive multiples by counting in equal steps, linking each entry with a multiplication fact for the given number.
Test whether a positive whole number is a multiple by dividing it by the given number and checking that no remainder remains.
Compare two ordered lists of multiples to find values that appear in both, continuing far enough to reach a shared value.
Distinguish the smallest positive common multiple from a later common multiple, and use any stated upper or lower limit to select an answer.
Recognise the relationship between factors and multiples: if one positive number divides another exactly, the second is a multiple of the first.
Does the answer make sense?
A proposed positive common multiple must divide exactly by each of the two given numbers. If the question asks for the smallest one, your child can also inspect every earlier entry in the shorter list of multiples and confirm that none is shared.
How to practise these questions
Basic questions find a numbered multiple or test whether a number belongs in a multiples list. Intermediate questions practise listing shared multiples below a limit, selecting a particular shared multiple and combining multiple conditions with an extra factor condition. The Challenge questions place a common multiple inside a numerical interval or give one numbered multiple and ask for another. Ask your child to identify the original step size before generating a list; for an unknown step, the position and value of a known multiple provide the starting information. Tick off each limit and divisibility condition against the answer. When several answers are requested, continue the ordered list to the stated boundary so that the response is complete. Its multiple-choice Basic questions ask which number is a common multiple of two given numbers, or which of four numbers is NOT a multiple of a given number.
Questions parents ask
How is a multiple different from a factor? A factor divides a number exactly, while a multiple is produced by multiplying that number by a whole number. The direction of the relationship matters. Ask your child which number is being multiplied or divided before deciding whether a list should contain factors or multiples.
Can my child multiply the two numbers to find the first common multiple? Their product is a common multiple, but it may not be the first positive one. Smaller shared values can occur when the numbers have a factor in common. Listing the multiples in order allows your child to see which shared value is reached first.
Why do the lists begin with the number itself? For these counting tasks, the list starts with the positive multiples: one group, two groups, three groups and so on. Zero is a multiple too, but it does not answer a request for the next repeated event or a positive quantity. Read any limits in the question carefully.
