Every year more then 2 to 3 questions form LCM and HCF are asked in SSC CGL, MTS, and CHSL Examination. LCM, and HCF Question are also Asked in UPSC NDA Examination and other Civil service Examination. If you cover this portion perfectly then you can easily correct 2- 3 Questions in these type of competitive Examination. IBPS also asked questions from LCM and HCF in bank PO, Clerk, Specialist officer and other Examination. Railway Recruitment Board also asked questions from Lowest Common Factor and Highest Common Factor.

What is HCF : The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers. In other words the H.C.F is the largest of all the common factors. The common factors or of 12 and 18 are 1, 2, 3 and 6. The largest common factor is 6, so this is the H.C.F. of 12 and 18. this is also known as mahttam samapvartak in Hindi Math.

What is LCM : A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, .... The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. This is also known as Laghuttam Samapvartak.

Question From महत्तम समापवर्तक (HCF) और लघुत्तम समापवर्त्य (LCM )

What is HCF : The Highest Common Factor (H.C.F) of two (or more) numbers is the largest number that divides evenly into both numbers. In other words the H.C.F is the largest of all the common factors. The common factors or of 12 and 18 are 1, 2, 3 and 6. The largest common factor is 6, so this is the H.C.F. of 12 and 18. this is also known as mahttam samapvartak in Hindi Math.

What is LCM : A common multiple is a number that is a multiple of two or more numbers. The common multiples of 3 and 4 are 0, 12, 24, .... The least common multiple (LCM) of two numbers is the smallest number (not zero) that is a multiple of both. This is also known as Laghuttam Samapvartak.

Question From महत्तम समापवर्तक (HCF) और लघुत्तम समापवर्त्य (LCM )

Q1. Find the H.C.F. of 204, 1190 and 1445.

(a) 17 (b) 14 (c) 25 (d) 27

Ans. (a)

Q2. Reduce 391/667 to lowest terms.

(a) 17/29 (b) 14/29 (c) 21/7 (d) 27/29

Ans. (a)

Q3. Find the H.C.F. of 2/3, 8/9, 10/27 and 16/81.

(a) 1/18 (b) 2/81 (c) 3/18 (d) 1/81

Ans. (b)

Q4. Find the L.C.M. of 2/3, 8/9, 10/27 and 16/81.

(a) 80/1 (b) 80/7 (c) 80/3 (d) 80/5

Ans. (c)

Q5. Two numbers are in the ratio 8:11, if their H.C.F is 6, find the numbers.

(a) 17, 48 (b) 14, 66 (c) 66, 25 (d) 48, 66

Ans. (d)

Q6. Four electronic devices make a beep after every 30 minutes, 1 hour, 1 1/2 hour and 1 hour 45 min respectively. All the devices beeped together at 12 noon. At what time will they beep together again?

(a) 10 a.m. (b) 9 a.m. (c) 7 a.m. (d) 8 a.m.

Ans. (b)

Q7. Find the largest number which can exactly divide 513, 783 and 1107.

(a) 28 (b) 24 (c) 26 (d) 27

Ans. (d)

Q8. Find the smallest number exactly divisible by each one of the numbers 12, 15, 20 and 27.

(a) 540 (b) 640 (c) 320 (d) 270

Ans. (a)

Q9. Find the least number which when divided by 6, 7, 8, 9,12 leaves the same remainder 2 in each case.

(a) 506 (b) 504 (c) 508 (d) 510

Ans. (a)

Q10. Find the largest natural number which exactly divides the product of any 4 consecutive natural numbers.

(a) 27 (b) 24 (c) 25 (d) 27

Ans. (b)

Q11. Find the least number which when divided by 35, 45 and 55 leaves the

Remainder 18, 28 and 38 respectively.

(a) 3444 (b) 3445 (c) 3448 (d) 3447

Ans. (c)

Q12. The simplest form of 69/92 is:

(a) 2/3 (b) 3/4 (c) 13/24 (d) none of these

Ans. (b)

Q13. The simplest form of 561/748 is:

(a) 13/14 (b) 11/14 (c) 23/24 (d) 3/4

Ans. (d)

Q14. 1095/1168 in simplest form is:

(a) 13/16 (b) 17/26 (c) 15/16 (d) 25/26

Ans. (c)

Q15. 128352/238368 when reduced to its lowest terms is:

(a) 3/4 (b) 7/13 (c) 9/13 (d) 5/13

Ans. (b)

Q16. The HCF of 1485 and 4356 is:

(a) 189 (b) 89 (c) 99 (d) 83

Ans. (c)

Q17. The HCF of 42, 63 and 140 is:

(a) 14 (b) 9 (c) 21 (d) 7

Ans. (d)

Q18. 252 can be expressed as a product of primes as

(a) 2*2*2*3*7 (b) 3*3*3*3*7 (c) 2*2*3*3*7 (d) 2*3*3*3*7

Ans. (c)

Q19. The HCF of 1134, 1344 and 1512 is:

(a) 24 (b) 42 (c) 44 (d) 64

Ans. (b)

Q20. The HCF of 1/2, 2/3, 3/4, 4/5 is:

(a) 1 (b) 12 (c) 4/5 (d) 1/60

Ans. (d)

Q21. The HCF of 2/3, 8/9, 10/27, 32/81 is:

(a) 160/81 (b) 160/3 (c) 2/81 (d) 2/3

Ans. (c)

Q22. Which of the following is a pair of co-primes?

(a) (14, 35) (b) (18, 25) (c) (31, 93) (d) (32, 62)

Ans. (b)

Q23. LCM of 87 and 145 is:

(a) 870 (b) 1305 (c) 435 (d) 1740

Ans. (c)

Q24. LCM of 22, 54, 108, 135, and 198 is:

(a) 330 (b) 1980 (c) 5940 (d) 11880

Ans. (c)

Q25. The LCM of 26, 56, 104, 182 is:

(a) 456 (b) 728 (c) 748 (d) 1274

Ans. (b)

Q26. The LCM of 3/4, 6/7, 9/8 is:

(a) 18 (b) 3 (c) 3/56 (d) 9/28

Ans. (a)

Q27. The LCM of 2/3, 4/9, 5/6, 7/12 is:

(a) 1/18 (b) 1/36 (c) 35/9 (d) 140/3

Ans. (d)

Q28. The LCM of two numbers is 2310 and their HCF is 30. If one of these numbers is 210. The second number is:

(a) 330 (b) 1470 (c) 2100 (d) 16170

Ans. (a)

Q29. The LCM of two numbers is 12 times their HCF. The sum of HCF and LCM is 403. If one number is 93, then the other is:

(a) 12 (b) 124 (c) 134 (d) none of these

Ans. (b)

Q30. The sum of two numbers is 45. Their difference is 1/9 of their sum. Their LCM is

(a) 100 (b) 150 (c) 200 (d) 250

Ans. (a)

Q31. The HCF and LCM of two numbers are 21 and 4641 respectively. If one of the numbers lies between 200 and 300. then the two numbers are:

(a) 273, 363 (b) 273, 359 (c) 273, 361 (d) 273, 357

Ans. (d)

Q32. The HCF of two numbers (each greater than 13) be 13 and LCM 273,

then sum of the numbers will be:

(a) 286 (b) 130 (c) 288 (d) 290

Ans. (b)

Q33. Two 3-digit numbers have their HCF 29and LCM 4147. the sum of the numbers is:

(a) 66 (b) 669 (c) 696 (d) 966

Ans. (c)

Q34. The ratio between two numbers is 2:3. If their LCM is 150, then the numbers are:

(a) 30, 40 (b) 48, 64 (c) 50, 75 (d) none of these

Ans. (c)

Q35. The ratio between two numbers is 15;11. If their HCF is 13, then the numbers are:

(a) 75, 55 (b) 105, 77 (c) 15, 11 (d) 195, 143

Ans. (d)

Q36. The HCF of two numbers is 8. Which of the following numbers cannot be the LCM of these numbers?

(a) 24 (b) 48 (c) 56 (d) 60

Ans. (d)

Q37. If two numbers are in the ratio of 2:3and the product of their HCF and LCM is 33750, then the sum of the numbers is:

(a) 250 (b) 325 (c) 375 (d) 425

Ans. (c)

Q38. The sum of two numbers is 216 and their HCF is 27. The numbers are:

(a) 54, 162 (b) 108,108 (c) 27, 189 (d) none of these

Ans. (c)

Q39. About the number of pairs of numbers which have 16 as their HCF and 136 as their LCM, we can definitely say that:

(a) only one such pair exits (b) Only two such pairs exist (c) many such pairs exist (d) no such a pair exists

Ans. (d)

Q40. The HCF and LCM of two numbers x and y are respectively 3 and 105, If x+y – 36, then 1/x + 1/y = ?

(a) 35 (b) 3/5 (c) 4/35 (d) 1/35

Ans. (c)

Q41. The HCF of three numbers is 12, If they are in the ratio 1:2:3, then the numbers are:

(a) 6, 12, 18 (b) 10, 20, 30 (c) 12, 24, 36 (d) 24, 48, 72

Ans. (c)

Q42. The sum of two numbers is 528 and their HCF is 33. The number of such pairs is:

(a) 2 (b) 3 (c) 4 (d) 5

Ans. (c)

Q43. The product of two co-primes is 117. Their LCM should be

(a) 1 (b) 117 (c) equal to their HCF (d) Cannot be calculated

Ans. (b)

Q44. The HCF of two numbers is 24. The number which can be their LCM is:

(a) 84 (b) 120 (c) 128 (d) 148

Ans. (b)

Q45. Three numbers are in the ratio 3:4:5 and their LCM is 2400. Their HCF is:

(a) 40 (b) 80 (c) 120 (d) 200 (e) none of these

Ans. (a)

Q46. The LCM of two prime numbers x and y (x>y) is 161. The value of (3y-x) is:

(a) -2 (b) -1 (c) 1 (d) 2

Ans. (a)

Q47. Which of the following fractions is the largest?

(a) 7/8 (b) 13/16 (c) 31/40 (d) 63/80

Ans. (a)

Q48. The largest number that divides 210, 315, 147 and 168 exactly is:

(a) 3 (b) 7 (c) 21 (d) 4410

Ans. (c)

Q49. A bell rings every 5 minutes. A second bell rings every 6 minutes and if the two bells ring at the same time in the morning, then the next time they will ring together at

(a) 8:30 o’clock (b) 9 o’ clock (c) 10 o’ clock (d)12 o’ clock

Ans. (a)

Q50. The traffic lights at three different road crossings change after every 48 seconds, 72 seconds and 108 seconds respectively. If they all change simultaneously at 8:20 hours, then at what time will they again change simultaneously?

(a) 8: 27: 12 hours (b) 8: 27: 24 hours (c) 8: 27: 36 hours (d) 8: 27: 48 hours

Ans. (a)

Q51. An electronic device makes a beep after every 60 sec. Another device makes a beep after every 62 sec. They beeped together at 10 a.m. The next time, when they would beep together at the earliest, is

(a) 10:30 a.m. (b) 10:31 a.m. (c) 10:59 a.m. (d) 11 a.m.

Ans. (b)

Q52. 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?

(a) 26 min18 sec (b) 42 min 36 sec (c) 46 min 12 sec (d) 45 min

Ans. (c)

Q53. A, B and C go walking round a circle 1 km in circumference at the rates of 10m/min, 20m/min and 40m/min respectively. If they all start together and walk in the same direction, when will they be together at the same place?

(a) after 50 min (b) after 100 min (c) after 240 min (d) after 800 min

Ans. (b)

Q54. The largest number which divides 77, 147 and 252 to leave the same remainder in each case is:

(a) 9 (b) 15 (c) 25 (d) 35

Ans. (d)

Q55. The greatest number of 5 digits, which is divisible by 15, 36, 21 is

(a) 99459 (b) 99540 (c) 99979 (d) 99999

Ans. (b)

Q56. What is the least number which when divided by 8, 9, 12, 15 leaves a reminder 1 in each case?

(a) 179 (b) 181 (c) 359 (d) 361

Ans. (d)

Q57. What is the least number which when diminished by 5, is divisible by each one of 21, 28, 36, 45?

(a) 425 (b) 1259 (c) 1260 (d) 1265

Ans. (d)

Q58. What is the least number which when increased by 7, is divisible by each one of 24, 32, 36, 54?

(a) 867 (b) 857 (c) 425 (d) 4318

Ans. (b)

Q59. What is the least multiple of 7 which when divided by each one of 6, 9, 15, 18 gives remainder 4 in each case?

(a) 74 (b) 94 (c) 184 (d) 364

Ans. (d)

Q60. What is the least number which when divided by 5, 6, 8, 9, 12 gives remainder 1 in each case and is completely divisible by 13?

(a) 361 (b) 721 (c) 1801 (d) 3601

Ans. (d)

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