HCF and LCM : 10 Questions Repeated in the Exams

Ques 1.

Six bells commencing tolling together toll at intervals of 2, 3, 6, 8 , 10 and 12 seconds respectively.In 30 minutes how many times do they toll together?
Ans 1. L.C.M of 2, 4, 6, 8, 10 and 12  is 120.
so, the bells will toll together after 120 seconds i.e. 2 minutes .
In 30 minutes the bells toll together 30/2 + 1 times i.e. times.

Ques 2.

The H.C.F of two numbers is 11 and their L.C.M is 7700. If one of these numbers is 275, then find the other number.
Ans 2. Product of two number s = product of their H.C.F. and L.C.M.
  required  number = 11 X 7700/275 = 308

Ques 3.

A gardener had a number of shrubs to plant in rows . At first he tried to plant 8, then 12 and then 16 in a row but he always had 3 shrubs left with him . On trying 7 shrubs he was left with none.Find the total number of shrubs.
Ans 3. L.C.M of 8,12,16 = 48
Now, 48 x 1 + 3 = 51 - not divisible by 7
48 x 2 + 3 = 99 - not divisible by 7
48 x 3 + 3 = 147 - not divisible by 7
  Required number = 147

Ques 4.

Three measuring rods are 64 cm,80 cm and 96 cm in length . What is the least length of cloth that can can be measured exact number of times using any one of these rods?
(a) 9.60 m
(b) 8 m
(c) 9.60 cm
(d) 96 m
Ans 4.  9.60 m

Ques 5.

The sum of two numbers is 528 and their H.C.F is 33. What is the number of pairs of such numbers ?
(a) 4
(b) 12
(c) 8
(d) 6
Ans 5.
Hint : Let  the number be 33x and 33y where x and y are co-prime.

Ques 6.

The largest numbers which divides 30, 78 and 102 to leave the same remainder in each case is
(a)24
(b) 20
(c) 8
(d) 16
Ans 6. 24

Ques 7.

Find the least number of five digits which is exactly divisible by 12, 15 and 18.
(a) 1080
(b) 10080
(c) 10025
(d) 11080
Ans 7. 10080
Hint : The least number of 5 digits is 10000. L.C.M. of 12, 15 and 18 is 180 . On dividing 10000 is 100.
=> 10000 + 180- 100 = 10080 is divisible by 180.

Ques 8.

The smallest number which when divided by 20, 25, 35 and 40 leaves a remainder of 14, 19 , 29 and 34 respectively is
(a) 1994
(b) 1494
(c) 1394
(d) 1496
Ans 8. 1394
Hint: Note that 20 -4 = 6; 25 -19 = 6;35-29= 6;40- 34 = 6
  Required number = L.C.M. of ( 20, 25, 35  and 40)-6

Ques 9.

Find the greatest unit of time with which 5 hours 15 minutes and 8 hours 24 minutes can both be represented as integers.
(a) 70 min.
(b) 63 min.
(c) 48 min.
(d) 42 min.
Ans 9.  63  min.

Ques 10.

The L.C.M of two numbers is 14 times their H.C.F . The sum of the L.C.M. and the H.C.F . is 600. If one number is 280 , then the other number is
(a) 40
(b) 60
(c) 80
(d) 100
Ans 10.  80

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