Question 8 - Figure it out - Page 122, 123 - Chapter 5 Class 8 - Number Play (Ganita Prakash)

Transcript

Question 8 Find a number that leaves a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5. What is the smallest such number? Can you give a simple explanation of why it is the smallest?Let's look at the remainders closely: Divide by 3, remainder 2. (This means the number is 1 less than a multiple of 3). Divide by 4, remainder 3. (This means the number is 1 less than a multiple of 4). Divide by 5, remainder 4. (This means the number is 1 less than a multiple of 5). Since the number is always "1 less" than a perfect multiple… If we just add 1 to our mystery number, it would be perfectly divisible by 3, 4, and 5! Now, the number perfectly divisible by 3, 4 and 5 is LCM of 3, 4, 5 Finding LCM of 3, 4, and 5 Thus, LCM =2 × 2 × 3 × 5 = 60 So, we can write Mystery number + 1 = 60 Mystery number = 60 - 1 Mystery number = 59 Now, we need to answer Can you give a simple explanation of why it is the smallest? Because 60 is the Least Common Multiple. Any other number would have to be based on larger multiples like 120, 180, etc.