Prime Factors, HCF & LCM (Cambridge (CIE) O Level Maths): Exam Questions

Find the highest common factor (HCF) of 90 and 48.

Write 56 as a product of its prime factors.

Find the lowest common multiple (LCM) of 56 and 42.

Trams leave Piccadilly

to Eccles every 9 minutes
to Didsbury every 12 minutes

A tram to Eccles and a tram to Didsbury both leave Piccadilly at 9 am.

At what time will a tram to Eccles and a tram to Didsbury next leave Piccadilly at the same time?

$A=3^2\times 5^4\times 7B=3^4\times 5^3\times 7\times 11$

Find the highest common factor (HCF) of $A$ and $B$.

Find the lowest common multiple (LCM) of $A$ and $B$.

$$\begin{gathered} A=3^5\times 5\times 7^3 \\ B=2^3\times 3\times 7^4 \end{gathered}$$

i) Find the Highest Common Factor (HCF) of $A$ and $B$.

[1]

ii) Find the Lowest Common Multiple (LCM) of $A$and $B$.

[1]

Work out the lowest common multiple (LCM) of 36 and 120.

$$\begin{gathered} \begin{array}{rcl}& & A=2^3\times 3^2\times 5^2\times 11 \\ B=2^4\times 3\times 5^4\times 13\end{array} \end{gathered}$$

Find the lowest common multiple (LCM) of $A$and $B$.
Give your answer as a product of powers of prime numbers.

Work out the lowest common multiple (LCM) of 120 and 144.

Find the highest odd number that is a factor of 60 and a factor of 90.

Buses to Acton leave a bus station every 24 minutes. Buses to Barton leave the same bus station every 20 minutes.

A bus to Acton and a bus to Barton both leave the bus station at 9 00 am.

When will a bus to Acton and a bus to Barton next leave the bus station at the same time?

Express 180 as a product of its prime factors.

Martin thinks of two numbers.

He says,

"The Highest Common Factor (HCF) of my two numbers is 6 The Lowest Common Multiple (LCM) of my two numbers is a multiple of 15"

Write down two possible numbers that Martin is thinking of.

Find the lowest common multiple (LCM) of 40 and 56.

$A=2^3\times 3\times 5B=2^2\times 3\times 5^2$

Write down the highest common factor (HCF) of A and B.

A machine has a buzzer that sounds every 50 minutes.
The machine also has a bell that sounds every 80 minutes.

The buzzer and the bell sound together at 10 am.

Find the time at which they next sound together.

Written as the product of its prime factors

$672=2^5\times 3\times 7$

Write 252 as the product of its prime factors.

Work out the value of the highest common factor of 672 and 252.

Here are three lamps.

Lamp A flashes every 20 seconds.
Lamp B flashes every 45 seconds.
Lamp C flashes every 120 seconds.

The three lamps start flashing at the same time.

How many times in one hour will the three lamps flash at the same time?

Write 720 as a product of its prime factors.
Show your working clearly.

Find the smallest whole number that 720 can be multiplied by to give a square number.

Find the highest common factor $\left(\mathrm{HCF}\right)$ of $96$ and $120$.

$\begin{array}{rcl}A& =& 2^3\times 5\times 7^2\times 11\\ B& =& 2^4\times 7\times 11\\ C& =& 3\times 5^2\end{array}$

Find the lowest common multiple $\left(\mathrm{LCM}\right)$ of $A,B$ and $C.$

$\begin{array}{rcl}A& =& 3^5\times 5\times 7^3\\ B& =& 2^3\times 3\times 7^4\\ C& =& 2^p\times 5^q\times 7^r\end{array}$

Given that

the HCF of $B$ and $C$ is 2³× 7
the LCM of $A$ and $C$ is 2⁴× 3⁵× 5²× 7³

Find the value of $p,$ the value of $q$ and the value of $r$.

$p=$ ....................................................... 
$q=$ ....................................................... 
$r=$ ....................................................... 

i) Write 84 as a product of its prime factors.

[1]

ii) $N$ is a two-digit number.
The lowest common multiple (LCM) of 84 and $N$ is 504.

Find $N$.

$N$ = ...........................[2]