\begin{tabular}{l} 4. Two lights flicker next to each other. One light flashes every 6 minutes and \\ the other light flashes every 4 minutes. How long will it take for the lights to \\ flicker at the same time? \\ \hline\end{tabular}

To determine how long it will take for the two lights to flicker at the same time, we need to find the least common multiple (LCM) of the two flashing intervals: 6 minutes and 4 minutes. ### Step 1: Identify the intervals - Light A flashes every \( a = 6 \) minutes. - Light B flashes every \( b = 4 \) minutes. ### Step 2: Find the LCM The LCM of two numbers 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. ### Step 3: Calculate the GCD To find the GCD of 6 and 4, we can list the factors: - Factors of 6: 1, 2, 3, 6 - Factors of 4: 1, 2, 4 The greatest common factor is 2. ### Step 4: Calculate the LCM Now we can calculate the LCM: \[ \text{LCM}(6, 4) = \frac{6 \times 4}{\text{GCD}(6, 4)} = \frac{24}{2} = 12 \] ### Conclusion The two lights will flicker at the same time after \( 12 \) minutes.