Real Numbers Practice 2: HCF, LCM and Applications

Section A: Core Skills

Question 1mcq

Find the HCF of

48

and

72

using prime factorisation.

A.

12

B.

36

C.

24

D.

144

Question 2mcq

Find the LCM of

12

and

18

.

A.

6

B.

36

C.

24

D.

72

Question 3mcq

Using

84=2^2\timesimes3\timesimes7

and

126=2\timesimes3^2\timesimes7

, what is their HCF?

A.

42

B.

21

C.

84

D.

252

Question 4mcq

Using

84=2^2\timesimes3\timesimes7

and

126=2\timesimes3^2\timesimes7

, what is their LCM?

A.

42

B.

252

C.

126

D.

504

Question 5mcq

For two positive integers

a

and

b

, when is

\timesext{HCF}(a,b)\timesimes\timesext{LCM}(a,b)=a\timesimes b

valid?

A.Only when

a

and

b

are prime

B.Only when

a

and

b

are co-prime

C.For every pair of positive integers

a

and

b

D.Only when

a=b

Section B: Application Problems

Question 6mcq

If the HCF of two numbers is

18

and their LCM is

180

, and one number is

90

, what is the other number?

A.

18

B.

45

C.

54

D.

36

Question 7mcq

Three ropes of lengths

24

m,

36

m, and

60

m are cut into equal pieces with no length left over. What is the greatest possible length of each piece?

A.

6

m

B.

12

m

C.

18

m

D.

24

m

Question 8mcq

Three bells ring every

12

,

15

, and

20

minutes. If they ring together at

8:00

a.m., when will they next ring together?

A.

8:30

a.m.

B.

8:45

a.m.

C.

10:00

a.m.

D.

9:00

a.m.

Question 9mcq

A teacher has

96

pencils and

120

erasers. She wants identical gift packs with no item left over. What is the maximum number of packs she can make?

A.

24

B.

12

C.

48

D.

30

Question 10mcq

A traffic light turns green every

45

seconds and another every

75

seconds. They turn green together now. How many times will they turn green together in the next

15

minutes, not counting now?

A.

3

B.

5

C.

4

D.

6