8
Question 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?
The expression of a number that leaves a remainder of 2 when divided by 3. Number = 3K + 2 3 × 1 + 2 = 5 3 × 2 + 2 = 8 3 × 3 + 2 = 11 3 × 4 + 2 = 14 3 × 5 + 2 = 17 3 × 6 + 2 = 20 The expression of a number that leaves a remainder of 3 when divided by 4. Number = 4K + 3 4 × 1 + 3 = 7 4 × 2 + 3 = 11 4 × 3 + 3 = 15 4 × 4 + 3 = 19 The expression of a number that leaves a remainder of 4 when divided by 5. Number = 5K + 4 5 × 1 + 4 = 9 5 × 2 + 4 = 14 5 × 3 + 4 = 19 5 × 4 + 4 = 24 Smallest number = LCM of (3, 4, 5) – 1 = 60 – 1 = 59 59 is the smallest 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. 5.2 Checking Divisibility Quickly Figure It Out (Page 126)