# HCF and LCM Questions Answers

1) Find the LCM of \begin{aligned} \frac{2}{3}, \frac{4}{6}, \frac{8}{27} \end{aligned}

- 1) \begin{aligned} \frac{2}{27} \end{aligned}
- 2) \begin{aligned} \frac{8}{3} \end{aligned}
- 3) \begin{aligned} \frac{2}{3} \end{aligned}
- 4) \begin{aligned} \frac{8}{27} \end{aligned}

**Ans.**B

**Explanation :**

Whenever we have to solve this sort of question, remember the formula. LCM = \\begin{aligned} \\frac{HCF of Denominators}{LCM of Numerators} \\end{aligned} So answers will be option 2, Please also give attention to the difference in formula of HCF and LCM

2) Find the HCF of 2.1, 1.05 and 0.

- 1) 0.44
- 2) 0.64
- 3) 0.21
- 4) None of above

**Ans.**C

**Explanation :**

To solve this question quickly, first remove decimal by multiplying each term with 100, Then terms become 210, 105, 63 Then HCF of above terms is 21, So Answer is 0.21

3) If LCM of two number is 693, HCF of two numbers is 11 and one number is 99, then find ot

- 1) 34
- 2) 77
- 3) 12
- 4) 45

**Ans.**B

**Explanation :**

For any this type of question, remember Product of two numbers = Product of their HCF and LCM So Other number = \begin{aligned} \frac{693 \times 11}{99} \end{aligned} = 77

4) LCM of two numbers is 7700 and HCF is 11. If one number is 308 then other number

- 1) 269
- 2) 285
- 3) 300
- 4) 275

**Ans.**D

**Explanation :**

5) Which greatest possible length can be used to measure exactly 15 meter 75 cm, 11 meter 25 cm and 7 meter 65

- 1) 45cm
- 2) 255cm
- 3) 244cm
- 4) 55cm

**Ans.**A

**Explanation :**

Convert first all terms into cm. i.e. 1575 cm, 1125cm, 765cm. Now whenever we need to calculate this type of question, we need to find the HCF. HCF of above terms is 255.

6) Find the greatest number which on dividing 1661 and 2045, leaves a reminder of 10 and 13 respectiv

- 1) 125
- 2) 127
- 3) 129
- 4) 131

**Ans.**B

**Explanation :**

In this type of question, its obvious we need to calculate the HCF, trick is HCF of (1661 - 10) and (2045 -13) = HCF (1651, 2032) = 127

7) Find the largest number which divides 62,132,237 to leave the same remin

- 1) 30
- 2) 32
- 3) 35
- 4) 45

**Ans.**C

**Explanation :**

Trick is HCF of (237-132), (132-62), (237-62) = HCF of (70,105,175) = 35

8) If the product of two numbers is 84942 and their H.C.F. is 33, find their L.C

- 1) 2574
- 2) 2500
- 3) 1365
- 4) 1574

**Ans.**A

**Explanation :**

HCF * LCM = 84942, because we know Product of two numbers = Product of HCF and LCM LCM = 84942/33 = 2574

9) Find the largest number of four digits which is exactly divisible by 27,18,12

- 1) 9700
- 2) 9710
- 3) 9720
- 4) 9730

**Ans.**C

**Explanation :**

LCM of 27-18-12-15 is 540. After dividing 9999 by 540 we get 279 remainder. So answer will be 9999-279 = 9720

10) Six bells commence tolling together and toll at the intervals of 2,4,6,8,10,12 seconds resp. In 60 minutes how many times they will toll togeth

- 1) 15
- 2) 16
- 3) 30
- 4) 31

**Ans.**D

**Explanation :**

LCM of 2-4-6-8-10-12 is 120 seconds, that is 2 minutes. Now 60/2 = 30 Adding one bell at the starting it will 30+1 = 31