1.3 Prime Factors, HCF & LCM

Use this information to write 438 048 as a product of its prime factors.

, where  is an integer and  is a square number.
 
Find the smallest value of .
 

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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?

Liz buys packets of coloured buttons.

There are 8 red buttons in each packet of red buttons.
There are 6 silver buttons in each packet of silver buttons.
There are 5 gold buttons in each packet of gold buttons.

Liz buys equal numbers of red buttons, silver buttons and gold buttons.

How many packets of each colour of buttons did Liz buy?

.................................... packets of red buttons

.................................... packets of silver buttons

.................................... packets of gold buttons

Ali is planning a party.

He wants to buy some cakes and some sausage rolls.

The cakes are sold in boxes.
There are 12 cakes in each box.
Each box of cakes costs £2.50

The sausage rolls are sold in packs.
There are 8 sausage rolls in each pack.
Each pack of sausage rolls costs £1.20

Ali wants to buy more than 60 cakes and more than 60 sausage rolls.
He wants to buy exactly the same number of cakes as sausage rolls.

What is the least amount of money Ali will have to pay?

John buys some boxes of pencils and some packets of pens for people to use at a conference.

There are 40 pencils in a box.
There are 15 pens in a packet.

John gives one pencil and one pen to each person at the conference.
He has no pencils left.
He has no pens left.

How many boxes of pencils and how many packets of pens did John buy?

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

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

and are integers such that




Find the highest common factor (HCF) of and
Give your answer as a product of powers of its prime factors.

Find the highest common factor  of and .

Find the lowest common multiple  of  and 

Given that

the HCF of and is 2³× 7
the LCM of and is 2⁴× 3⁵× 5²× 7³

Find the value of the value of and the value of .

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 is a number.

As a product of prime factors in index form    

Work out as a product of prime factors in index form.

Give your answer in terms of .

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.

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?

Rita is going to make some cheeseburgers for a party.
She buys some packets of cheese slices and some boxes of burgers.

There are 20 cheese slices in each packet.
There are 12 burgers in each box.

Rita buys exactly the same number of cheese slices and burgers.

i)  How many packets of cheese slices and how many boxes of burgers does she buy?

Rita wants to put one cheese slice and one burger into each bread roll.
She wants to use all the cheese slices and all the burgers.

ii) How many bread rolls does Rita need?

Matt and Dan cycle around a cycle track.

Each lap Matt cycles takes him 50 seconds.
Each lap Dan cycles takes him 80 seconds.

Dan and Matt start cycling at the same time at the start line.

Work out how many laps they will each have cycled when they are next at the start line together.

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 highest common factor (HCF) of 72 and 90.

Find the highest common factor (HCF) of  and .

Find the lowest common multiple (LCM) of  and .

Find the Highest Common Factor (HCF) of and .

[1]

Find the Lowest Common Multiple (LCM) of and .

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

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

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.

Work out the highest common factor (HCF) of 75 and 105.

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

Written as the product of its prime factors

Write 252 as the product of its prime factors.

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