1. **State the problem:** Find the least common multiple (LCM) of 250 and 140. 2. **Recall the formula:** The LCM of two numbers $a$ and $b$ can be found using the formula: $$\text{LCM}(a,b) = \frac{|a \times b|}{\text{GCD}(a,b)}$$ where GCD is the greatest common divisor. 3. **Find the GCD of 250 and 140:** - Prime factorization of 250: $250 = 2 \times 5^3$ - Prime factorization of 140: $140 = 2^2 \times 5 \times 7$ - Common prime factors: $2$ and $5$ - GCD is the product of the lowest powers of common primes: $2^1 \times 5^1 = 10$ 4. **Calculate the LCM:** $$\text{LCM}(250,140) = \frac{250 \times 140}{10} = \frac{35000}{10} = 3500$$ 5. **Conclusion:** The least common multiple of 250 and 140 is **3500**.