While Preparing for** Quantitative aptitude tests,** questions on Number system- HCF and LCM are asked frequently.

**Top 10 HCF and LCM Questions**

**Q1) Two numbers are in the ratio 2 : 3. If their L.C.M. is 48. what is sum of the numbers?**

A) 64

B) 42

C) 28

D) 40

**Solution :**

**Q2) What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?**

A) 9200

B) 9600

C) 9800

D) 9400

**Solution :**

**Q3) Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:???????**

A) 40

B) 20

C) 10

D) 30

**Solution :**

**Q4) What is the lowest common multiple of 12, 36 and 20?**

A) 120

B) 160

C) 220

D) 1

**Solution :**

**Q5) H.C.F. of 513, 1134 and 1215 is _____________ **

A) 18

B) 27

C) 33

D) 36

**Solution : **

We know different methods to calculate H.C.F.

Finding H.C.F. by division method:

H.C.F. of 513, 1134 and 1215 = 3 × 3 × 3 = 27.

**Q6) The greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively, is: **

A) 127

B) 305

C) 235

D) 123

**Solution :**

Required number = H.C.F. of (1657 - 6) and (2037 - 5)

= H.C.F. of 1651 and 2032 = 127.

**Q7) The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: **

A) 276

B) 299

C) 322

D) 345

**Solution :**

Clearly, the numbers are (23 x 13) and (23 x 14).

Larger number = (23 x 14) = 322.

**Q8) HCF of 3/16, 5/12, 7/8 is: **

A) 2/47

B) 3/47

C) 1/48

D) 5/48

**Solution :**

**HCF of numerators = 1 **

LCM of denominators = 48

=> 1/48

**Q9) The least number, which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 8 is: **

A) 544

B) 548

C) 504

D) 536

**Solution :**

Required number = (L.C.M. of 12, 15, 20, 54) + 8 = 540 + 8 = 548.

**Q10) Find the lowest common multiple of 24, 36 and 40. **

A) 120

B) 240

C) 360

D) 480

**Solution :**