EXERCISE LCM of \( 2 \times 3 \times 5 \) and \( 3 \times 5 \times 7 \) is equal to \( \begin{array}{ll}\text { (A) } 3 & \text { (B) } 3 \times 5 \\ \text { (C) } 2 \times 3 \times 5 \times 7 & \text { (D) } 2 \times 3 \times 5 \times 3 \times 5 \times 7\end{array} \)

To find the least common multiple (LCM) of the two numbers \( 2 \times 3 \times 5 \) and \( 3 \times 5 \times 7 \), we first identify the prime factors involved in both numbers. 1. The first number is \( 2 \times 3 \times 5 \). - Prime factors: \( 2, 3, 5 \) 2. The second number is \( 3 \times 5 \times 7 \). - Prime factors: \( 3, 5, 7 \) Next, we take the highest power of each prime factor that appears in either number: - For the prime factor \( 2 \): The highest power is \( 2^1 \) (from the first number). - For the prime factor \( 3 \): The highest power is \( 3^1 \) (appears in both numbers). - For the prime factor \( 5 \): The highest power is \( 5^1 \) (appears in both numbers). - For the prime factor \( 7 \): The highest power is \( 7^1 \) (from the second number). Now, we can calculate the LCM by multiplying these highest powers together: \[ \text{LCM} = 2^1 \times 3^1 \times 5^1 \times 7^1 = 2 \times 3 \times 5 \times 7 \] Thus, the LCM of \( 2 \times 3 \times 5 \) and \( 3 \times 5 \times 7 \) is \( 2 \times 3 \times 5 \times 7 \). Looking at the options provided: - (A) \( 3 \) - (B) \( 3 \times 5 \) - (C) \( 2 \times 3 \times 5 \times 7 \) - (D) \( 2 \times 3 \times 5 \times 3 \times 5 \times 7 \) The correct answer is: \[ \boxed{2 \times 3 \times 5 \times 7} \]