Question 17 of 18intermediate🔧 ApplyNumerical2 marks

What is the smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10? Do you remember the answer from Grade 6, Chapter 5?

Correct Answer

Given: Find the smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10.

Formula: The smallest number that is a multiple of given numbers is their LCM.

Step 1: LCM(1, 2, 3, 4, 5, 6, 8, 9, 10) = LCM(2, 3, 4, 5, 6, 8, 9, 10)

Step 2: Prime factorisations: 2 = 2 3 = 3 4 = 2² 5 = 5 6 = 2×32 \times 3 8 = 2³ 9 = 3² 10 = 2×52 \times 5

Step 3: Maximum powers: 2³, 3², 5¹

Calculation: LCM = 2³ × 3² × 5 = 8×98 \times 9 × 5 = 360

Answer: 360

Exercise: Figure it Out (Section 6) | Q: 21 | (Page Page 18)
For More Understanding

Explanation

To find the smallest number divisible by all given numbers, we find their LCM. We take the highest power of each prime that appears in any factorisation: 2³ (from 8), 3² (from 9), and 5¹ (from 5 and 10). LCM = 8×98 \times 9 × 5 = 360.

Solution Steps

  1. Step 1: List prime factorisations: 2=2, 3=3, 4=2², 5=5, 6=2×32 \times 3, 8=2³, 9=3², 10=2×52 \times 5.

  2. Step 2: Find maximum power of each prime: 2³, 3², 5.

  3. Step 3: LCM = 2³ × 3² × 5 = 8×98 \times 9 × 5 = 360.

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