Class 6 Mathematics Sindh Textbook Exercise 3.6 Solved Notes

Exercise 3.6 Solved

Question 1

Find the greatest length of a wooden scale that can measure 540 cm and 360 cm exactly.

Solution

Required length = HCF (540,360)

HCF = 180 cm

Question 2

Find the greatest number that divides 232 and 305, leaving remainders 7 and 5 respectively.

Solution

232 − 7 = 225

305 − 5 = 300

Required HCF = HCF (225,300)

= 75

Question 3

Find the largest number which divides 245 and 1029, leaving remainder 5 in each case.

Solution

245 − 5 = 240

1029 − 5 = 1024

HCF (240,1024)

= 16

Question 4

Two tankers contain 600 litres and 570 litres of petrol.

Find the maximum capacity of a container that can measure both exactly.

Solution

Required HCF (600,570)

= 30 litres

Question 5

The length, breadth and height of a room are 8 m, 6 m, and 4 m.

Find the longest tape that can measure all dimensions exactly.

Solution

Required HCF (8,6,4)

= 2 metres

Question 6

Three bells ring after every 5, 10 and 15 minutes.

If they start ringing together at 8:00 A.M., when will they ring together again?

Solution

Required LCM

LCM (5,10,15)

= 30 minutes

Time

8:00 + 30 minutes

Answer = 8:30 A.M.

Important Formulas

Highest Common Factor (HCF)

The greatest number that divides all given numbers exactly.

Least Common Multiple (LCM)

The smallest number that is exactly divisible by all given numbers.

Relationship Between HCF and LCM

$$\boxed{\text{Product of Two Numbers}=\text{HCF}\times\text{LCM}}$$

Conclusion

Exercises 3.4, 3.5, and 3.6 introduce students to Highest Common Factor (HCF), Least Common Multiple (LCM), and their applications in real-life problems. By practicing prime factorization, long division, and word problems, students develop a strong understanding of number operations that prepares them for higher-level mathematics.