Class 6 Mathematics Sindh Textbook Exercise 3.5 Solved Notes

Exercise 3.5 Solved

Exercise 3.5 Solved

Question 1

Find the LCM using Prime Factorization.

(i) 12, 25, 40

12 = 2² × 3

25 = 5²

40 = 2³ × 5

LCM = 2³ × 3 × 5²

= 600

(ii) 21, 49, 63

21 = 3 × 7

49 = 7²

63 = 3² × 7

LCM = 3² × 7²

= 441

(iii) 144, 180, 384

144 = 2⁴ × 3²

180 = 2² × 3² × 5

384 = 2⁷ × 3

LCM = 2⁷ × 3² × 5

= 5760

(iv) 108, 135, 162

108 = 2² × 3³

135 = 3³ × 5

162 = 2 × 3⁴

LCM = 2² × 3⁴ × 5

= 1620

(v) 35, 65, 75

35 = 5 × 7

65 = 5 × 13

75 = 3 × 5²

LCM = 3 × 5² × 7 × 13

= 6825

(vi) 24, 36, 48, 72

24 = 2³ × 3

36 = 2² × 3²

48 = 2⁴ × 3

72 = 2³ × 3²

LCM = 2⁴ × 3²

= 144

Question 2

Calculate the LCM by Division Method

(i) 45 and 55

LCM = 495

(ii) 21, 35 and 70

LCM = 210

(iii) 24, 40 and 60

LCM = 120

(iv) 72, 108 and 120

LCM = 1080

Question 3

The product of two numbers is 360.

If their HCF = 12

Find the LCM.

Solution

Formula:

$$\text{Product}=\text{HCF}\times\text{LCM}$$ $$LCM=\frac{360}{12}=30$$

Conclusion

This chapter helps students understand factors, multiples, divisibility rules, prime numbers, composite numbers, and prime factorization. Mastering these concepts builds a strong foundation for higher mathematics and algebra.