 # LCM and HCF aptitude questions

LCM and HCF is a topic that needs to be understood thoroughly and clearly. Questions in this section can sometimes be tricky as well as time-consuming. So, make sure that you practice different level of questions in order to have flexibility while solving problems related to this concept.

Important topics covered in this section are Factors, Multiples, calculating LCM & HCF of a given number, co-primes, etc. To make your preparation easy we have compiled the most important 20 questions from this topic. Make sure you dedicate considerable time to solve these questions with integrity.

We assume that you have completed Number system practice before coming to this page, if not make sure you solve questions from number system first. Second, after you complete this section solve questions from decimal fraction

If you are already thorough with all the concepts of quantitative aptitude then move on to reasoning ability and verbal ability

Q1

The L.C.M. of three different numbers is 120.  Which of the following cannot be their H.C.F.?

Level 1 HCF and LCM Basic Concept of LCM and HCF
A

8

B

12

C

24

D

35

Q2

A number less than 500, when divided by 4,5,6,7 leaves remainder 1 in each case. The number is

Level 1 HCF and LCM Basic Concept of LCM and HCF Division Remainder and Word Problems
A

211

B

420

C

421

D

441

Q3

The H.C.F. of two numbers, each having three digits is 17 and their L.C.M.  is 714. Find the sum of the numbers.

Level 2 HCF and LCM Basic Concept of LCM and HCF
A

102

B

119

C

221

D

211

Q4

The LCM of two numbers is 48. The numbers are in the ratio 2:3. The sum of the numbers is:

Level 1 HCF and LCM Basic Concept of LCM and HCF
A

28

B

32

C

40

D

64

Q5

The sum of two numbers is 45. Their difference is $\frac{1}{9}$ of their sum. Their L.C.M. is

Level 1 HCF and LCM Basic Concept of LCM and HCF
A

100

B

150

C

200

D

250

Q6

The LCM of 22, 54, 108, 135 and 198 is:

Level 1 HCF and LCM Basic Concept of LCM and HCF
A

330

B

1980

C

5940

D

11880

Q7

$\frac{1095}{1168}$ when expressed in simplest form is:

Level 1 HCF and LCM Fractions Decimals and Ratios Basic Concept of LCM and HCF
A

13/16

B

15/16

C

17/26

D

25/26

Q8

Reduce $\frac{128352}{238368}$ to its lowest terms

Level 1 HCF and LCM Fractions Decimals and Ratios Basic Concept of LCM and HCF
A

3/4

B

5/13

C

7/13

D

9/13

Q9

The L.C.M. of $\frac{3}{4}$,$\frac{6}{7}$,$\frac{9}{8}$ is

Level 1 HCF and LCM Fractions Decimals and Ratios Basic Concept of LCM and HCF
A

3

B

6

C

9

D

18

Q10

Three numbers are in the ratio 1:2:3 and their HCF is 12. The numbers are

Level 1 HCF and LCM Fractions Decimals and Ratios Basic Concept of LCM and HCF
A

4,8,12

B

5,10,15

C

10,20,30

D

12,24,36

Q11

Which of the following fractions is the largest?

Level 1 HCF and LCM Fractions Decimals and Ratios
A

$\frac{7}{8}$

B

$\frac{13}{16}$

C

$\frac{31}{40}$

D

$\frac{63}{80}$

Q12

The ratio of two numbers is 3:4 and their HCF is 4. Their LCM is

Level 1 HCF and LCM Basic Concept of LCM and HCF Fractions Decimals and Ratios
A

12

B

16

C

24

D

48

Q13

Find the greatest number which on dividing 1657 and 2037 leaves remainder 6 and 5 respectively

Level 1 HCF and LCM Division Remainder and Word Problems Basic Concept of LCM and HCF
Q14

A milkman has 3 jars containing 57 litres, 129 litres and 177 litres of pure milk respectively.  A measuring can, after a different number of exact measurements of milk in each jar, leaves the same amount of milk unmeasured in each jar. What is the volume of the largest such can?

Level 2 HCF and LCM Division Remainder and Word Problems
A

12 litres

B

16 litres

C

24 litres

D

none of these

Q15

The least number which when divided by 5,6,7 and 8 leaves remainder 3, but when divided by 9 leaves no remainder is

Level 2 HCF and LCM Division Remainder and Word Problems
A

1677

B

1683

C

2523

D

3363

Q16

A, B and C start at the same time in the same direction to run around a circular stadium. A completes a round in 252 seconds, B in 308 seconds and C in 198 seconds, all starting at the same point. After what time will they meet again at the starting point?

Level 1 HCF and LCM Division Remainder and Word Problems Basic Concept of LCM and HCF
A

26 minutes 18 seconds

B

42 minutes 36 seconds

C

45 minutes

D

46 minutes 12 seconds

Q17

What is the greatest number of 3 digits which when divided by 6,9 and 12 leaves a remainder of 3 in each case, is

Level 2 HCF and LCM Division Remainder and Word Problems
A

903

B

939

C

975

D
996
Q18

The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

Level 2 HCF and LCM Division Remainder and Word Problems
A

74

B

94

C

184

D

364

Q19

The number nearest to 43582 divisible by each of 25,50 and 75 is

Level 2 HCF and LCM Division Remainder and Word Problems
A

43500

B

43550

C

43600

D

43650

Q20

The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:

Level 2 HCF and LCM Division Remainder and Word Problems
A

74

B

94

C

184

D

364