LCM and HCF
Team Careers360, 18 Sep 2019

LCM and HCF - Least Common Multiple (LCM) & Highest Common Multiple (HCF) is the topic also related to numbers. These topics are generally asked in SSC & Railways exam. The questions may be directly based on the concept of LCM and HCF. If you master these topics, you can score well in the exam. The general questions asked from LCM and HCF in competitive exams are as follows:-

  1. Questions based on finding the LCM and HCF of numbers

  2. Questions based on LCM and HCF of fractions

  3. Questions based on the product formula of LCM and HCF

  4. Questions based on addition, subtraction, multiplication & division of the numbers

  5. Questions based on the ratio of the numbers, etc.

Questions related to these topics are usually repeated from questions asked in previous exams. The best way to have command over LCM and HCF is to make your concept clear by solving previously asked questions thoroughly. The concept of LCM and HCF can be used further in solving many other topics of Quantitative Aptitude. So, it is an important topic of competitive exam.

How to prepare LCM & HCF?

  • Clear the concept of number system before solving the questions of LCM and HCF.

  • Understand the difference between multiples and factors.

  • Practice the sample paper questions related to HCF and LCM.

  • Go through the questions of LCM & HCF appeared in the past papers.

Practice questions of LCM and HCF

Q 1. The \: sum\: of\: two\: numbers \: is \:243 \: and \: their \:HCF \: is \:27. \:The \:numbers \:are

  1. \left ( 81, 189 \right )

  2. \left ( 122, 121 \right )

  3. \left ( 27, 216 \right )

  4. \left ( 81, 152 \right )

  5. None of these

View Solution


Q 2. The\: HCF \:of\: two \:numbers\: is \:14 \:and\: their\:difference\:is \:14.

\:The \:numbers \: are:

  1. 64, 78

  2. 72, 86

  3. 70, 84

  4. 98, 122

  5. None of these

View Solution


Q 3. The HCF of two numbers is 11 and their LCM is 7700. One number is 308, the other number is:

  1. 280

  2. 238

  3. 275

  4. 318

  5. None of these

View Solution


Q 4. Product of two co-prime numbers is 143, their LCM should be:

  1. 1

  2. 143

  3. Equal \: to \: HCF

  4. Can't \: be\: determined

  5. 134

View Solution


Q 5. Two number, both greater than 29, have GCD = 29 and LCM = 4147. The sum of the numbers is:

  1. 669

  2. 696

  3. 766

  4. 767

  5. None of these

View Solution


Q 6. The greatest possible length which can be used to measure exactly the lengths: 20 m 6 cm, 11m 90 cm and 14 m 45 cm is:

  1. 17

  2. 18

  3. 19

  4. 121

  5. None of these

View Solution


Q 7.What is the maximum number of students among whom 1095 pens and 1168 pencils can be distributed in such a way that each student gets the equal number of pens and equal number of pencils.

  1. 71

  2. 73

  3. 63

  4. 65

  5. None of these

View Solution


Q 8. Find the greatest number that will divide 48, 97 and 188 and leaves the remainder 6 in each case.

  1. 4

  2. 7

  3. 2

  4. 6

  5. None of these

View Solution


Q 9. The greatest number, which when divides 1358, 1870, and 2766 leaves the same remainder 14 in each case, is:

  1. 124

  2. 64

  3. 156

  4. 260

  5. None of these

View Solution


Q 10. What will be the least number which when doubled becomes exactly divisible by 9, 15, 21, and 30?

  1. 196

  2. 189

  3. 630

  4. 315

  5. None of these

View Solution


Q 11. The\: least \: five \: digit \: number \: which \: is \: exactly\: divisible\: by \: 12, 18,\: and\: 21 \: is

  1. 10010

  2. 10015

  3. 10080

  4. 10020

  5. None of these

View Solution


Q 12. The \: greatest\: four\: digit \: number \: which \: is \: divisible\: by \: 18, 25, 30, \: and \: 48 \: is

  1. 9000

  2. 9200

  3. 7200

  4. 9729

  5. None of these

View Solution


Q 13. The smallest number which when diminished by 5 becomes divisible by 12, 16, 18, 21, and 28

  1. 1015

  2. 1013

  3. 1022

  4. 1017

  5. None of these

View Solution


Q 14. The \: least \: number \: which \: when \: increased \: by \:7 \:becomes \: divisible \:by \: 24, 32, 36, \: and \:54

  1. 427

  2. 854

  3. 857

  4. 859

  5. None of these

View Solution


Q 15. Find the least multiple of 23 which when divided by 24, 21, and 18 leaves the remainders 13, 10, and 7 respectively

  1. 3004

  2. 3024

  3. 3013

  4. 3026

  5. None of these

View Solution


Q 16. The least number which when divided by 5, 6, 7, and 8 leaves the remainder 3. But when divided by 9 leaves no remainder, is:

  1. 1766

  2. 1683

  3. 2327

  4. 1895

  5. None of these

View Solution


Q 17. Four different devices beep after every half hour, 60 min, 1 and half hours, and 135 min respectively. All the devices beeped together at 12 noon. They will beep together again at:

  1. 12 \: midnight

  2. 6 \: AM

  3. 9 \: PM

  4. 7:30\: AM

  5. None of these

View Solution


Q 18. X, Y, Z start at the same time in the same direction to run around a circular stadium. X completes a round in 63 seconds, Y in 105 seconds and Z in 210 seconds. If they start at the same time, then at what time will they meet again at the starting point?

  1. 9 \: min \: 9 \: seconds

  2. 10 \: min\: 30\: seconds

  3. 10\: min \: 6 \: seconds

  4. 8 \: min \: 4 \: seconds

  5. None of these

View Solution


Q 19. On Ashok Marg three consecutive traffic lights change after 36, 42 and 72 seconds respectively. If the lights are first switched on at 9:00 A.M. sharp, at what time will they change simultaneously?

  1. 9 : 08 : 04

  2. 9 : 08 : 24

  3. 9 : 08 : 44

  4. None\: of\: these

  5. None of these

View Solution


Q 20. Two numbers are in the ratio 17:13. If their HCF is 15, what are the numbers?

  1. 255, 195

  2. 265, 185

  3. 135, 39

  4. None\: of\: these

  5. Data insufficient

View Solution


Q 21. The HCF and LCM of two numbers are 33 and 264 respectively. When the first number is divided by 2, the quotient is 33. The other number is?

  1. 112

  2. 132

  3. 198

  4. 99

  5. None of these

View Solution


Q 22. Which of the following represents the largest 4 digit number which can be added to 7249 in order to make the derived number divisible by each of 12, 14, 21, 33 and 54.

  1. 9222

  2. 9383

  3. 8727

  4. None \: of\: these

  5. 9300

View Solution


Q 23. Find the greatest number of four digits which when divided by 10, 11, 15, and 22 leaves 3, 4, 8 and 15 as remainders respectively.

  1. 9907

  2. 9902

  3. 9903

  4. 9100

  5. None\: of\: these

View Solution


Q 24. Find the greatest number, which will divide : 215,\:167 \:and \:135 \:so\:as \:to\:leave\: the same remainder in each case.

  1. 64

  2. 32

  3. 24

  4. 16

  5. None of these

View Solution


Q 25. The L.C.M of \: 4.5, 0.009,\: and \: 0.18 =?

  1. 4.5

  2. 0.255

  3. 2.25

  4. 45

  5. None of these

View Solution

Preparation
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