QUESTION 2 2.1 Determine the LCM and HCF of the numbers 20 and 45 . 2.2 A motorist covers a distance of 360 Km in exactly 4 hours. 2.2. How far did the motorist drive in 1 hour? 2.2.2 How far will the motorist drive in 7 hours? 2.2.3 How long will the motorist need to travel 900 Km ?

Sure, let's solve each part of the question step by step. --- ### **2.1 Determine the LCM and HCF of the numbers 20 and 45.** **HCF (Highest Common Factor)** and **LCM (Least Common Multiple)** are two fundamental concepts in number theory. **Step 1: Find the Prime Factors** - **Prime factors of 20:** - 20 ÷ 2 = 10 - 10 ÷ 2 = 5 - 5 is a prime number. - So, 20 = 2 × 2 × 5 = 2² × 5¹ - **Prime factors of 45:** - 45 ÷ 3 = 15 - 15 ÷ 3 = 5 - 5 is a prime number. - So, 45 = 3 × 3 × 5 = 3² × 5¹ **Step 2: Determine HCF** The HCF is the product of the lowest powers of common prime factors. - Common prime factor: **5** - Lowest power of 5 in both numbers: 5¹ **HCF = 5** **Step 3: Determine LCM** The LCM is the product of the highest powers of all prime factors present in the numbers. - Prime factors involved: 2, 3, 5 - Highest powers: - 2² (from 20) - 3² (from 45) - 5¹ (common in both) **LCM = 2² × 3² × 5¹ = 4 × 9 × 5 = 180** --- ### **2.2 A motorist covers a distance of 360 Km in exactly 4 hours.** First, let's determine the motorist's speed. **Speed = Distance ÷ Time** **Speed = 360 Km ÷ 4 hours = 90 Km/hour** --- #### **2.2.1 How far did the motorist drive in 1 hour?** Since the motorist's speed is 90 Km/hour: **Distance = Speed × Time** **Distance = 90 Km/hour × 1 hour = 90 Km** --- #### **2.2.2 How far will the motorist drive in 7 hours?** **Distance = Speed × Time** **Distance = 90 Km/hour × 7 hours = 630 Km** --- #### **2.2.3 How long will the motorist need to travel 900 Km?** **Time = Distance ÷ Speed** **Time = 900 Km ÷ 90 Km/hour = 10 hours** --- ### **Summary** - **HCF of 20 and 45:** 5 - **LCM of 20 and 45:** 180 - **Distance driven in 1 hour:** 90 Km - **Distance driven in 7 hours:** 630 Km - **Time to travel 900 Km:** 10 hours