Page 50 - Maths Class 06

SO LU TION : The re quired min i mum dis tance each should walk is the LCM of three mea sures.
Thus, we shall find the LCM of 80, 85 and 90.
Now, 80 = 2 2 2 2 5´ ´ ´ ´

85 = 5 17´
90 = 2 3 3 5´ ´ ´

\ LCM = ´ ´ ´ ´ ´ ´ ´2 2 2 2 3 3 5 17 = 12240
Hence, the required distance is 12240 cm or 122.4 m.

Exercise 3.6

1. Deter mine the two numbers near est to 10000 which are exactly divis i ble by each of 2, 3, 4, 5, 6
and 7.
2. Determine the greatest 5-digit number which is exactly divisible by each of 8, 15 and 21.

3. Ananya saves ` 4.65 daily. Find the least number of days in which she will be able to save an exact
number of rupees.

4. Find the small est number which when divided by 25, 40, 60 leaves a remain der of 7 in each case.
5. Two tank ers contain 700 and 750 litres of milk respec tively. Find the maxi mum capac ity of a
container which can measure the milk of each tanker in exact number of times.

6. There are 312, 260 and 156 students in class VI, VII and VIII respec tively. Buses are to be hired to
take the students to a picnic. Find the maxi mum number of students who can sit in a bus, if each
bus takes equal number of students. Also, find the number of buses required.

7. The length, breadth and height of a room are 6 m 30 cm, 5 m 85 cm and 3 m 60 cm respec tively.
What will be the great est length of a tape which can measure the dimen sions of the room in exact
number of times?

[Hint : Convert the dimensions into cm and then find the HCF]
8. Find the greatest number which exactly divides 40 and 87 leaving remainders 4 and 3
respectively.
9. In a morn ing walk, three boys step off together from the same spot. Their steps measure 63 cm,
70 cm and 77 cm respec tively. What is the mini mum distance each should cover, so that all can
cover the distance in complete steps?
10. Three boxes of books contain 24, 40 and 56 books. These books are to be packed in small pack ets
which will contain equal number of books. What is the largest number of books that can be
packed in each of the small packets?

11. A rectangular court yard is 20 m 16 cm long and 15 m 60 cm broad. It is to be paved with
square-shaped tiles of the same size. Find the number of tiles required to pave the court yard.

12. The circum fer ence of the wheels of a carrier are 3 m 25 cm and 5 m. What is the least distance in
which both wheels make an exact number of revolutions?

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