GENERAL KNOWLEDGE

Problems on LCM and HCF

Q.1. Two numbers are in the ratio 2 : 3. If their L.C.M. is 48. What is sum of the numbers?

a)       28       b) 40     c) 64      d) 42      e) 32

Ans: b

Explanation:

Let the two numbers be 2x and 3x respectively.

LCM of 2x and 3x = 6x

Given, 6x = 48

So, x = 8

The required sum = 2x + 3x = 16 + 24 = 40. Ans.

     Q.2. What is the greatest number of four digits which is divisible by 15, 25, 40 and 75 ?

             a) 9800     b) 9600     c) 9400       d) 9200       e) 9000

              Ans: b

             Explanation:

             The greatest 4- digit number = 9999

             LCM of 15, 25, 40 and 75 = 600

            The remainder obtained when 9999 is divided by 600 = 399

            Therefore, the required greatest number = 9999 – 399 = 9600 Ans.

     Q.3. 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) 30        c) 20    d) 10      e) None of these

           Ans: c

            Explanation :

Let the numbers be 2x, 3x and 4x

LCM of 2x, 3x and 4x = 12x

=> 12x = 240

=> x = ²⁴⁰⁄₁₂ = 20

H.C.F of 2x, 3x and 4x = x = 20

     Q.4.  Find the minimum number of square tiles required to pave the floor of a room of 2m 50cm   long and 1m 50cm broad ?

a)      50      b) 750      c) 45       d) 15     e) None of these

          Ans: d

          Explanation:

  HCF of 250 cm and 150 cm is 50 cm, which is the side of the tile

So, the required number of tiles  =  (250 × 150) / (50 × 50)  =  15