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

  

Q.5. What is the least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder?      a) 1108     b) 1683      c) 2007         d) 3363    e) None of these     Ans: b    Explanation:    Just see which of the given choices satisfy the given conditions Take 3363. This is not even divisible by 9. Hence this is not the answer Take 1108. This is not even divisible by 9. Hence this is not the answer Take 2007. This is divisible by 9. 2007 ÷ 5 = 401, remainder = 2 . Hence this is not the answer Take 1683. This is divisible by 9. 1683 ÷ 5 = 336, remainder = 3 1683 ÷ 6 = 280, remainder = 3 1683 ÷ 7 = 240, remainder = 3 1683 ÷ 8 = 210, remainder = 3 Hence 1683 is the answer     Q.6. Find the HCF of   22×32, 2×34×7   a) 128       b) 126       c) 146       d) 434    e) 148   Ans: b   Explanation:   HCF is Highest common factor, so we need to get the common highest factors among given values. So we got                       2 × 3×3 × 7 = 126   Q.7.  Find the HCF of 54, 288, 360    a) 18    b) 36      c) 54     d) 108    e) 72    Ans: a    Explanation:    Let’s solve this question by factorization method. 54 =2×33,  288 = 25×32,  360 = 23×32×5   So HCF will be minimum term present in all three, i.e. 2×32=18   Q.8.  Reduce  368/575  to the lowest terms.       a) 30/25      b)  28/29          c) 16/25     d) 11/12    e) 13/15    Ans: c    Explanation:      We can do it easily by in two steps      Step1: We get the HCF of 368 and 575 which is 23      Step2: Divide both by 23, we will get the answer 16/25 Q. 9. Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are            a) 12, 24, 36   b) 5, 10, 15    c) 4, 8, 12      d) 6, 8, 13    e) 10, 20, 30 Ans: a Explanation: Numbers are 1 × 12, 2 × 12 and 3× 12                      i.e. 12, 24 and 36 Q.10. Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case.            a) 4   b) 5    c) 7     d) 9       e) 13 Ans: Explanation: Required number = HCF of ( 91 – 43), (183 – 91)   and (183 – 43)                              = HCF of 48, 92, 140                              = 4