L.C.M and H.C.F Important Questions

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1. LCM of  \frac{2}{3}, \frac{4}{9}\frac{5}{6} is

(a) \frac{8}{27}                      (b)\frac{20}{3}

(c)   \frac{10}{3}                     (d)\frac{20}{27}

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

(a) 180              (b) 176

(c)  182             (d) 178

3.The greatest number by which 2300 and 3500 are divided  leaving the remainders of 32 and 56 respectively:

(a) 168              (b)  42

(c)   48              (d)  136

4.Let x be the smallest number,  which when added to 2000 makes the resulting number   divisible by 12, 16, 18 and 21. The sum of the digits of x is

(a)  6  (b)  5   (c)  7   (d)  5

5. Let x be the least number, Which when divided by 5, 6, 7  and 8 leaves a remainder 3 in  each case but when divided by  9 leaves remainder zero. The sum  of the digits of x is

(a)  24  (b)  21  (c)  22  (d)  18

6. A number when divided by 361 gives remainder 47. When the same number is divided by 19,  then find the remainder?

(a)  9   (b)  1  (c)  8  (d)  3

7. The HCF and LCM of two  numbers are 21 and 84 repectively. If the ratio of two numbers is 1:4, then the larger of the two numbers is

(a)  48  (b)  12  (c)  84   (d)  108

8. The LCM of two numbers is 12 times their HCF. The sum of   the HCF and LCM is 403. If one of the number is 93, then the  other is

(a)  116             (b)  124

(c)  112             (d)  120

9. The number of pairs of positive  integers whose sum is 99 and HCF is 9 is :

(a)  5             (b)  2

(c)  3              (d)  4

10.The ratio of two numbers is 3 :  4 and their LCM is 120. The sum of numbers is:

(a)  70          (b)  35

(c)  140        (d)  105

11. The greatest 4 digit number  which is exactly divisible by each  one of the numbers 12, 18, 21 and   28.

(a)  9828             (b)  9882

(c)  9928             (d)  9288

12. The smallest five digit number which is divisible by 12, 18 and 21 is:

(a)  10080       (b)  30256

(c)  10224       (d)  50321

13.A number between 1000 and  2000 which when divided by 30,  36 and 80 gives a remainder 11  in each case is:

(a)  11523           (b)  1451

(c)  1641              (d)  1712

14. The difference between the greatest and least prime numbers which are less than 100 is

(a)  95               (b)  96

(c)  97                (d)  94

15. The number between 4000 and 5000 that is divisible by each   12, 18, 21 and 32 is

(a)  4203              (b)  4023

(c)  4032              (d)  4302

16. The ratio of HCF and LCM of  two numbers a and b is 1 : 30 and the difference between the  HCF and LCM is 493. Find the possible number of pairs of a and b.

(a)  one            (b)  Two

(c)  Four           (d) Five

17. The LCM of four consecutive numbers is 60. The sum of the first two numbers is equal to  the fourth number. What is the  sum of four numbers?

(a)  17              (b)  14

(c)  21               (d)  24

18.If the product of three  consecutive numbers is 210 then the sum of the smaller numbers is:

(a) 3                (b)  4

(c)  5                (d) 11

19. Three bells rings at interval of 36 seconds, 40 seconds and 48 seconds respectively. They start ringing together at a particular time. They will ring together after every

(a)  6 minutes

(b)  12 minutes

(c)  18 minutes

(d)  24 minutes

20. Two pipes of length 1.5 m and 1.2 m are to be cut into equal pieces without leaving any extra length of pipes. The greatest length of the pipe pieces of same size which can be cut from these two lengths will be

(a)  0.13m            (b)  26m

(c)  0.3 m              (d)  0.41 m

21. A General of an Army wants to create a formation of square from 36562 army men. After arrangement, he found some army men remained unused.

(a)   36              (b)  65

(c)  81                (d)  97

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