hcf and lcm no calculator 3r1 exam-type questions_hcf_and_lcm.pdf · the lowest common multiple...

HCF AND LCM EXAM-TYPE QUESTIONS

NO CALCULATOR Ref: G131.3R1

© 2018 Maths4Everyone.com Worksheets, Videos, Interactive Quizzes and Exam Solutions

A1 Express 204 as a product of its prime factors. Show your working clearly.

A2 Write 792 as a product of its prime factors. Show your working clearly.

A3 1400 = 2p × 52 × 7 Find the value of p.

A4 Given that 120 = 23 × 3 × 5 And that n = 120 × 108 Write n as a product of powers of its prime factors.

B1 Find the highest common factor (HCF) of 90 and 252

B2 Find the lowest common multiple (LCM) of 24 and 42

B3 Find the highest common factor (HCF) and lowest common multiple (LCM) of 168 and 180

B4 Find the highest common factor (HCF) and lowest common multiple (LCM) of 72, 180 and 540

C1 A = 23 × 3 × 52 B = 22 × 3 Find the HCF and LCM of A and B.

C2 M = 24 × 32 × 7 N = 22 × 32 × 5 Find the HCF and LCM of M and N.

C3 2520 = 23 × 32 × 5 × 7 3024 = 24 × 33 × 7 Find the HCF & LCM of 2520 and 3024. Write your answer as a product of prime factors.

C4 740 880 = 24 × 33 × 5 × 73 980 100 = 22 × 34 × 52 × 112 Find the highest common factor (HCF) of 740 800 and 980 100

D1 The highest common factor (HCF) of 90 and x is 18 The lowest common multiple (LCM) of 90 and x is 540 Find the value of x.

D2 The highest common factor (HCF) of x and 12 is 6 The lowest common multiple (LCM) of x and 12 is 180 Find the value of x.

D3 Find two numbers between 100 and 150 that have a HCF of 22.

D4 360 = 24 × 32 × 5 Write down three different factors of 360 with a sum between 90 and 100.

HCF AND LCM[ESTIMATED TIME: 45 minutes] GCSE

(+ IGCSE) EXAM QUESTION PRACTICE

11

*P43130A01120* Turn over

(b) On the grid, draw a cumulative frequency graph for your table.

(2)

(c) Use your graph to find an estimate for the lower quartile of the lengths of time the 160 students exercised.

.. . . . . . . . . . . . . . . . . . . . . . . . . . minutes(2)

(Total for Question 10 is 5 marks)

11 Find the Lowest Common Multiple (LCM) of 20 and 24

... . . . . . . . . . . . . . . . . . . . . . . . .


Cumulative frequency

200

150

100

50

O 40 80 120 160 200 240Time (t minutes)

1. [2 marks]

Note that these questions are sorted in date order (most recent questions first).

January 2014, 3HR Q11: 2 Marks

9


10

Work out the value of x. Give your answer correct to 1 decimal place.

x =. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


11! "#$! %&'(!)*+!,&-*+.)!/0110'!%#2)03!",/%$!04!56!#'(!78

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

! "9$!%&'(!)*+!:0;+.)!/0110'!<=>)&?>+!":/<$!04!56!#'(!78

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


7@5!21

x°

8.3 cm

Diagram NOT accurately drawn

2. [4 marks]


May 2013, 3H Q11: 4 Marks

Questions compiled by:@Maths4Everyone

Contains questions which have been reproduced with the kindpermission of Pearson Education Limited UK

11


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10 The highest common factor (HCF) of 140 and x is 20

The lowest common multiple (LCM) of 140 and x is 420

Find the value of x.

x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


3. [2 marks]


June 2016, 4H Q10: 2 Marks

5. Express 504 as a product of powers of its prime factors.

............................................ (3)

6. S = 24 × 3 × 72 T = 2 × 53 ×73 Find the Highest Common Factor (HCF) of S and T.

............................................ (2)

4. [2 marks]


September by Maths4Everyone.com, Extra Q11: 2 Marks

11


(b) On the grid, draw a cumulative frequency graph for your table.

(2)

(c) Find an estimate for the upper quartile of the weights of the 180 letters.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . grams(2)


11 A = 23 ! 32 ! 54

B = 35 ! 5 ! 73

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

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


Cumulativefrequency

Weight (w grams)

200

150

100

50

O 20 40 60 80 100 120

5. [2 marks]


May 2013, 4HR Q11: 2 Marks

9


10 x 8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(ii) n is an integer.

Write down all the values of n n 8

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


11

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


Do NOT write in this space.

6. [4 marks]


January 2012, 4H Q11: 4 Marks

Leave blank

12

*H34885A01224*

11. (a) Find the Highest Common Factor of 64 and 80

......................................(2)

(b) Find the Lowest Common Multiple of 64 and 80

......................................(2)

12. (a) Expand and simplify (p + 7)(p 4)

......................................(2)

(b) Simplify 4x3y5 ! 3x2y

......................................(2)

(c) Simplify (27q6)23

......................................(2) Q12

(Total 6 marks)

Q11

(Total 4 marks)

7. [4 marks]


November 2009, 4H Q11: 4 Marks

11


(b) Find an estimate for the percentage of the 80 films that lasted more than 125 minutes.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . %(3)


11 x is an integer. The Lowest Common Multiple (LCM) of x and 12 is 120 The Highest Common Factor (HCF) of x and 12 is 4

Work out the value of x.

x = .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


8. [2 marks]


June 2015, 4H Q11: 2 Marks

10

*P44619A01020*

12 Here are the marks scored in a test by the girls in class 8C.

2 8 10 12 15 16 16 17 18 19 20

(a) Work out the interquartile range of the girls’ marks.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

The boys in class 8C did the same test. The boys’ marks had a range of 19 and an interquartile range of 11 marks.

Gareth says that the girls’ marks are more spread out than the boys’ marks.

(b) Is Gareth right?

Tick (9 ) the appropriate box.

Yes No

Give a reason for your answer.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(1)


13 Given that A 23 u 3 and B 22 u 32

find the Lowest Common Multiple (LCM) of A and B.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


9. [2 marks]


January 2015, 3HR Q13: 2 Marks

! = 2!!×!3!!×!7!

! = 2!!×!3!!×!5!

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

(2)

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

(2)

10. [4 marks]



12

*P44613A01224*

11

3780 = 22 × 33 × 5 × 7 3240 = 23 × 34 × 5

(a) Find the highest common factor (HCF) of 3780 and 3240 Give your answer as a product of prime factors.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)

(b) Find the lowest common multiple (LCM) of 3780 and 3240 Give your answer as a product of prime factors.

.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(2)


11. [4 marks]


January 2015, 3H Q11: 4 Marks

Leaveblank

14N17226A

14. (a) Find the Highest Common Factor of 75 and 105.

..........................

(2)

(b) Find the Lowest Common Multiple of 75 and 105.

..........................

(2)

15. Make v the subject of the formula m(v – u) = I

v = .................... Q15

(Total 3 marks)

Q14

(Total 4 marks)

12. [4 marks]



267!300 = 2!!×!3!!×!5!!×!11

246!960 = 2!!×!3!!×!5!×!7!

(a) Find the highest common factor (HCF) of 267 300 and 246 960 Give your answer as a product of prime factors. ............................................

(2) (b) Find the lowest common multiple (LCM) of 267 300 and 246 960 Give your answer as a product of prime factors. ............................................

(2) Solve 5x2 – 6x – 2 = 0 Give your solutions correct to 3 significant figures. Show your working clearly. ............................................

(3)

13. [4 marks]



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14. [4 marks]



SOLUTIONSHCF AND LCMIGCSE EXAM QUESTION PRACTICEGCSE (+ IGCSE) EXAM QUESTION PRACTICE

DATE OF SOLUTIONS: 15/05/2018

MAXIMUM MARK: 44

1. [Edexcel, 2014] HCF and LCM [2 Marks]

4. [New Question, by Maths4Everyone.com] HCF and LCM [2 Marks]

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