Primary School · Mathematics

Common multiples and Common factors: Practice Questions

5 multiple-choice questions marked as you go, and 5 written questions with worked solutions. All on Common multiples and Common factors.

10 questions27 marksFree, no account

Question 1

1 mark

Which of the following numbers is a common multiple of $6$ and $8$?

Question 2

1 mark

Two positive whole numbers, A and B, have a Highest Common Factor (H.C.F.) of $8$ and a Least Common Multiple (L.C.M.) of $144$.

If number $A$ must be greater than $10$ but less than $60$, what is the value of the sum $A + B$?

Question 3

1 mark

The product of two numbers is $$720$$. If their Least Common Multiple (LCM) is $$180$$, what is their Highest Common Factor (HCF)?

Question 4

1 mark

Which of the following numbers is a common multiple of $9$ and $12$?

Question 5

1 mark

First, find the Highest Common Factor ($\text{H.C.F.}$) of $48$ and $60$. Let this factor be $F$.

Next, find the second smallest positive whole number that is a common multiple of $F$ and $18$.

Question 6

3 marks

Find the first two common multiples of $9$ and $12$.

Write your answer out first, then check it against the worked solution.

Question 7

4 marks

Find the smallest common multiple of $12$ and $16$ that is greater than $100$.

Write your answer out first, then check it against the worked solution.

Question 8

5 marks

Let $H$ be the Highest Common Factor ($\text{H.C.F.}$) of the numbers 56, 84, and 140. Let $M$ be the Least Common Multiple ($\text{L.C.M.}$) of the numbers 12, 15, and 18.

Find the value of the smallest positive whole number that is a common multiple of $H$ and $M$. What is the sum of the digits of this resulting number?

Write your answer out first, then check it against the worked solution.

Question 9

5 marks

A florist is making bouquets. There are 20 lilies and 28 roses. The florist wants to group the flowers so that each bouquet has the same number of lilies and the same number of roses, with no flowers left over.

Part a: List all the possible numbers of bouquets the florist can make by finding all the common factors of $20$ and $28$.

Part b: What is the Highest Common Factor (H.C.F.) of $20$ and $28$?

Part c: Two flashing lights are turned on at the same time. Light A flashes every $8$ seconds and Light B flashes every $10$ seconds. After how many seconds will both lights next flash at the same time? (Find the Least Common Multiple (L.C.M.) of $8$ and $10$).

Write your answer out first, then check it against the worked solution.

Question 10

5 marks

A local bakery is managing production logistics involving common multiples and common factors for their goods.

Part A: Production Synchronization (L.C.M.)

Croissants are baked in batches of 15, and Muffins are baked in batches of 20. If the baker wants to produce the exact same total number of croissants and muffins, what is the smallest total number of croissants produced?

Let this minimum number be L.

Part B: Packaging Optimization (H.C.F.)

The baker has 90 Scones and 120 Brownies. She wants to divide all of them into the greatest possible number of identical display boxes, such that every box contains the same number of scones and the same number of brownies, with no leftovers. What is the greatest number of identical display boxes she can prepare?

Let this maximum number be H.

Part C: Combined Multiple Constraint

Find the second smallest positive common multiple of L (the number from Part A) and H (the number from Part B).

Write your answer out first, then check it against the worked solution.

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