This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Find the prime factorization of each number. 14 = 2 × 7 = 2^1 × 7^1 35 = 5 × 7 = 5^1 × 7^1 40 = 2 × 2 × 2 × 5 = 2^3 × 5^1 56 = 2 × 2 × 2 × 7 = 2^3 × 7^1 Step 2: Calculate the Least Common Multiple (LCM) of 14, 35, 40, and 56. The LCM is the product of all prime factors raised to their highest powers. The prime factors are 2, 5, 7. Highest power of 2 is 2^3. Highest power of 5 is 5^1. Highest power of 7 is 7^1. LCM(14, 35, 40, 56) = 2^3 × 5^1 × 7^1 = 8 × 5 × 7 = 40 × 7 = 280 Step 3: Set up the equation to find the required number. Let the required number be N. According to the problem, when 10 is added to N, the result is exactly divisible by 14, 35, 40, and 56. This means N + 10 must be equal to the LCM. N + 10 = LCM(14, 35, 40, 56) N + 10 = 280 Step 4: Solve for N. N = 280 - 10 N = 270 The least number is 270. Last free one today — make it count tomorrow, or type /upgrade for unlimited.