**Problems on LCM & HCF Aptitude Questions and Answers | MCQ Problems: **Take Problems on LCM and HCF Quiz Online Test right now through this post. Well, in the Aptitude Section, one of the well known and mostly asked areas is **LCM and HCF**. And many of the aspirants who are prepping for different kinds of Exams like the Staff Selection Commission, UPSC, SSSB, Police, Banks, Railways, RRB, IBPS, and many other Entrance Tests or Recruitment Tests can use the help. Well, preparing for the Problems on L.C.M and H.C.F Quiz is not that difficult task. All you have to know is some** Problems with LCM & HCF Aptitude Tricks** and shortcuts. That’s it. In no time you can surely top it. Now, through this post, we are going to provide information about the lcm and hcf problems with solutions pdf, lcm and hcf formulas, hcf and lcm problems, hcf and lcm aptitude tricks, lcm problems with solutions, lcm and hcf problems for bank PO. Check further.

## Problems on LCM and HCF Quiz

Quiz Name |
Problems on L.C.M and H.C.F |

Category |
Aptitude |

Number of Questions |
25 |

Time |
30 Minutes |

Exam Type |
MCQ (Multiple Choice Questions) |

## Problems on LCM and HCF Online Test – Practice Now

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**1. What is the H.C.F of 4/5, 6/8, 8/25.**

A. 1/200

B. 1/100

C. 1/5

D. 1/50

E. None

**Answer: B**

**Explanation: **

**2. The sum and difference of HCF and LCM of two numbers is 666 and 518. Find both the numbers if sum of these two numbers is 444.**

A. 296, 148

B. 74, 296

C. 122, 244

D. 122, 183

E. None

**Answer: A**

**Explanation: **

**3. Find the least number which when divided by 6, 7, 8, 9, and 12, leaves remainder 4 in each case?**

A. 504

B. 508

C. 606

D. 656

E. None

**Answer: B**

**Explanation:**

L.C.M of 6, 7, 8, 9, 12 = 504

∴ Least number for remainder as 4 = 508

**4. The least number, which when divided by 3, 5, 7, 6, 8 leaves a remainder of 2 in each case is.**

A. 212

B. 722

C. 842

D. 282

E. None

**Answer: C**

**Explanation:**

LCM of (3, 5, 6, 7, 8) = 840

Therefore, the number when divided by 3, 5, 7, 6, 8 leaves remainder 2

= 840 + 2 = 842

**5. The HCF of two numbers is 98 and their LCM is 2352. The sum of the numbers may be**

A. 1078

B.1398

C. 1426

D. 1484

E. None

**Answer: A**

**Explanation:**

Let two numbers are 98x and 98y. Then,

Product of number = Product of HCF and LCM

98x × 98y = 98 × 2352

xy = 24

Let x = 8 and y = 3 (As Co-prime factors of 24 be 8 and 3)

Then, Sum of number = 98 × 8 + 98 × 3 = 98 (11) = 1078

Hence, option A is correct.

**6. What will be the ratio of Highest common Factor and Least Common Multiple of two numbers 14 and 18?**

A. 1:49

B. 1:27

C. 1:21

D. 1:63

E. None

**Answer: D**

**Explanation:**

We will find common factor and common multiple of 14 and 18 respectively.

14 = 2 × 7 and 18 = 3 × 3 × 2

HCF = 2 and

LCM = 2 × 7 × 9 = 126

∴ HCF : LCM = 2 : 126 = 1 : 63

**7. In finding the HCF of 2 numbers by division method, the quotients are 3, 5 & 7 respectively, and the last divisor is 96. What is the sum of numbers?**

A. 12386

B. 13356

C. 14496

D. 15876

E. None

**Answer: C**

**Explanation:**

**8. What will be the Highest Common Factor of 5, 10 and 20?**

A. 5

B. 10

C. 1

D. 15

E. None

**Answer: A**

**Explanation: **

We will find common factors of 5, 10, and 20.

5 = 5 × 1

10 = 5 × 2

20 = 5 × 2 × 2

So, highest common factor will be 5.

**9. What will be the largest number which divides by 37, 66 and 89 leave a remainder of 2, 3 and 5 respectively?**

A. 14

B. 7

C. 5

D. 12

E. None

**Answer: B**

**Explanation: **

**10. Three natural number whose LCM is 360, are in the ratio 2:3:4, the largest of them is:**

A. 120

B. 60

C. 180

D. 240

E. None

**Answer: A**

**Explanation: **

**11. The least positive number which should be added to 2291 so that the sum is exactly divisible by 4, 5, 8 and 10?**

A. 29

B. 39

C. 19

D. 24

E. None

**Answer: A**

**Explanation:**

L.C.M of 4, 5, 8 and 10 = 40

Nearest number to 2291 which is completely divisible by 40 is 2320 and 2280

But here we are talking about adding a number so 2280 is rejected

hence required number = 2320-2291 = 29

**12. Let m be the least number divisible by 12,18,24,36,45, and m is also a perfect cube. What is the sum of digit of remainder when m is divided by 89?
**

A. 17

B. 9

C. 6

D. 4

E. None

**Answer: C**

**Explanation: **

**13. ****The least number which when divided by 6, 9, 12, 15, 18 leaves the same remainder 2 in each case, is:**

A. 176

B. 178

C. 180

D. 182

E. None

**Answer: D**

**Explanation:**

Given numbers are: 6, 9, 12, 15, 18

LCM of given numbers = 180

So, 180 + 2 = 182 is the number that leaves 2 as a remainder.

**14. Let m be the least number divisible by 12,18,24,30,36,45, and m is also a perfect square. What is the sum of digit of remainder when m is divided by 133?**

A. 12

B. 8

C. 13

D. 4

E. None

**Answer: C**

**Explanation: **

**15. Which is the smallest six-digits number, which when divided by 4, 8, 12, 15,18 and 20, leaves 7 as the remainder.**

A. 100082

B. 100092

C. 100057

D. 100087

E. None

**Answer: D**

**Explanation: **

**16. In finding the HCF of 2 numbers by division method, the quotients are 4, 2 & 8 respectively, and the last divisor is 72. What will be the difference between these two numbers?**

A. 3024

B. 3144

C. 2984

D. 3004

E. None

**Answer: A**

**Explanation: **

**17. Two numbers are in ratio 52 : 1 and their LCM is 884 then find the difference between their square.**

A. 751689

B. 781167

C. 811801

D. 799187

E. None

**Answer: B**

**Explanation: **

**18. Find the H.C.F. and L.C.M. of 0.63, 1.05 and 2.1.**

A. 0.21 and 6.30

B. 1.05 and 6.30

C. 2.1 and 0.63

D. 0.63 and 1.05

E. None

**Answer: A**

**Explanation:**

Making the same number of decimal places, the given numbers are 0.63, 1.05 and 2.10.

Without decimal places, these numbers are 63, 105 and 210.

Now, H.C.F of 63, 105 and 210 is 21.

∴ H.C.F, of 0.63, 1.05 and 2.1 is 0.21.

L.C.M. 63, 105 and 210 is 630

∴ L.C.M. of 0.63, 1.05 and 2.1 is 6.30.

**19. Find the largest number which divides 62, 132 and 237 to leave the same remainder in each case.**

A. 15

B. 25

C. 35

D. 55

E. None

**Answer: C**

**Explanation:**

Required number = H.C.F. of (132 – 62), (237 – 132) and (237 – 62)

= H.C.F. = 70, 105 and 175 = 35.

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## Factors and Multiples

Now, suppose A is divided by another number B exactly, then a is called a factor of b. And then b is considered as the multiple of a.

## Highest Common Factor (HCF) or Greatest Common Measure (GCM) or Greatest Common Divisor (G.C.D.)

So, the HCH of two or more numbers is the Greatest Number. And it divides them exactly. So, there are two methods to find the HCF of the given number one is the Factorization Method. Another is Division Method. Now, in the Case of the Factorization method, an individual can express the given number as the product of the prime factory. So, the product of the Least powered prime factors will give you the HCF. Now, to find the HCF of two given numbers, first, divide the Larger by the smaller. Then proceed and divide the divisor by the remainder. Now, continue this process till you get Remainder as Zero. So, now the last divisor is the HCF.

## Problems on LCM and HCF Tricks and Shortcuts

Now, finding HCF for more than two numbers or three numbers then following is the method

**H.C.F [(HCF of two number) and (third Number)]**

Now, in the same manner, an individual can get the HCF for more than three numbers too. Well, now coming to the case of the LCM. It is known as the Least Common Multiple. So, the least number that can exactly divisible by any of the given numbers is known as the LCM. Well, for calculating the LCM, there are also two different methods. Factorization as well as the Division method. Check the following set of Terms and Formulae.

**The product of two numbers = Product of their H.C.F. and L.C.M.****Co-primes: Two numbers are said to be co-prime if their H.C.F. is 1.**

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