O LevelMathsCambridgeTopic QuestionsNumberPrime Factors, HCF & LCM

Prime Factors, HCF & LCM (Cambridge O Level Maths)

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1
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Write 84 as a product of its prime factors.

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2
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Write 525 as a product of its prime factors.

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1
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Find the highest odd number that is a factor of 60 and a factor of 90.

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2
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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?

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3a
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Express 180 as a product of its prime factors.

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3b
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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.

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4a
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Find the lowest common multiple (LCM) of 40 and 56.

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4b
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A space equals space 2 cubed space cross times space 3 space cross times space 5 space space space space space space space space space space space space space space space space space space space space space space B space equals space 2 to the power of 2 space end exponent cross times space 3 space cross times space 5 squared

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

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5
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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.

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6a
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Written as the product of its prime factors

672 space equals space 2 to the power of 5 space end exponent cross times space 3 space cross times space 7

Write 252 as the product of its prime factors.

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6b
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Work out the value of the highest common factor of 672 and 252.

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1
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Find the highest common factor (HCF) of 90 and 48.

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2a
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Write 56 as a product of its prime factors.

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2b
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Find the lowest common multiple (LCM) of 56 and 42.

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3
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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?

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4a
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A equals space 3 squared space cross times space 5 to the power of 4 space cross times space 7 space space space space space space space space space space space space space space space space space space space space space B space equals space 3 to the power of 4 space cross times space 5 cubed space cross times space 7 space cross times space 11

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

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4b
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Find the lowest common multiple (LCM) of A and B.

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5
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A space equals space 3 to the power of 5 cross times space 5 space cross times space 7 to the power of 3 space end exponent B space equals space 2 cubed cross times space 3 space cross times space 7 to the power of 4

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

[1]

ii)
Find the Lowest Common Multiple (LCM) of space A spaceand B.
[1]

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6
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Work out the lowest common multiple (LCM) of 36 and 120.

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7
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table row blank blank cell A space equals space 2 cubed cross times 3 squared cross times 5 squared cross times 11 B space equals space 2 to the power of 4 cross times 3 cross times 5 to the power of 4 cross times 13 end cell end table

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

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8
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Work out the lowest common multiple (LCM) of 120 and 144.

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1
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Here are three lamps.

q4-1-3-hard-ocr-gcse-maths-extended

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?

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2a
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Write 720 as a product of its prime factors.
Show your working clearly.

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2b
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Find the smallest whole number that 720 can be multiplied by to give a square number.

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3a
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Find the highest common factor left parenthesis HCF right parenthesis of 96 and 120.

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3b
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table row cell A space end cell equals cell space 2 cubed space cross times space 5 space cross times space 7 squared space cross times space 11 space end cell row cell B space end cell equals cell space 2 to the power of 4 space cross times space 7 space cross times space 11 space end cell row cell C space end cell equals cell space 3 space cross times space 5 squared end cell end table

Find the lowest common multiple left parenthesis LCM right parenthesis of A comma space B and C.

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4
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table row cell A space end cell equals cell space 3 to the power of 5 cross times space 5 space cross times space 7 cubed space end cell row cell B space end cell equals cell space 2 cubed cross times space 3 space cross times space 7 to the power of 4 space end cell row cell C space end cell equals cell space 2 to the power of p cross times space 5 to the power of q cross times space 7 to the power of r end cell end table

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 comma the value of q and the value of r.

p space equals ....................................................... 
q space equals ....................................................... 
r space equals ....................................................... 

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