#### 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. **4

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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