Question 12 - Figure it out - Page 63, 64 - Chapter 3 Class 7 - Finding Common Ground (Ganita Prakash II)

Transcript

Question 12 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?We can do this by two methods Method 1 – Finding LCM of 1, 2, 3, 4, 5, 6, 8, 9, 10 Method 2 – Building the number Let’s do by both Method 1 Now, Smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10 = LCM of 1, 2, 3, 4, 5, 6, 8, 9, 10 Finding LCM Thus, LCM = 2 × 2 × 2 × 3 × 3 × 5 = 8 × 9 × 5 = 360 Thus, 360 is the smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10 1, 2, 3, 4, 5, 6, 8, 9, 10 1, 1, 3, 2, 5, 3, 4, 9, 5 1, 1, 3, 1, 5, 3, 2, 9, 5 1, 1, 3, 1, 5, 3, 1, 9, 5 1, 1, 1, 1, 5, 1, 1, 3, 5 1, 1, 1, 1, 5, 1, 1, 1, 5 1, 1, 1, 1, 1, 1, 1, 1, 1 Method 2 Smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10Here is a step-by-step way to build that number: Start with the largest number The number must be a multiple of 10. So, let's start with 10. The factors of 10 are 2 and 5. This means our final answer must be divisible by 2 and 5. Consider the next number 9 Our number must also be a multiple of 9. The factors of 9 are 3 & 3. Our current number (10) is not divisible by 9. To make it divisible by 9, we need to include its factors (3 × 3). So far, our number needs the factors: 2 × 5 × 3 × 3 = 90 Consider 8 Our number must be a multiple of 8. The factors of 8 are 2 × 2 × 2. Our current number (90) only has one factor of 2. To make it divisible by 8, it needs to have three factors of 2. We'll replace our single 2 with three 2s. Our factors are now: (2 × 2 × 2) × 3 × 3 × 5 = 360 Check the remaining numbers: Now we see if our new number, 360, is a multiple of the rest of the numbers on the list Is 360 a multiple of 6? 6 is 2 × 3. Our number has plenty of 2s and 3s. Yes, 360 ÷ 6 = 60. Is 360 a multiple of 5? Yes, it ends in 0. 360 ÷ 5 = 7 Is 360 a multiple of 4? 4 is 2 × 2. Our number has three 2s. Yes, 360 ÷ 4 = 90. Is 360 a multiple of 3? Yes, it has two 3s as factors. 360 ÷ 3 = 120. Is 360 a multiple of 2? Yes, it's an even number. 360 ÷ 2 = 180. Is 360 a multiple of 1? Yes, all whole numbers are. Since 360 is the smallest number we could build that satisfies all these conditions, the answer is 360.