Step-by-step Solution:

We calculate the lowest common multiple (LCM) of (24), (36), and (40) step-by-step using their prime factorizations.\[\] \[\] Step 1: Find the prime factorization of each number \[\] 1. (24 = 2^3 \(\times\) 3) \[\] 2. (36 = 2^2 \(\times\) 3^2) \[\] 3. (40 = 2^3 \(\times\) 5) \[\] \[\] Step 2: Identify the highest powers of all prime factors \[\] The prime numbers involved are (2), (3), and (5). From the factorizations:\[\] - For (2), the highest power is (2^3). \[\] - For (3), the highest power is (3^2). \[\] - For (5), the highest power is (5). \[\] \[\] Step 3: Write the LCM formula \[\] The LCM is given by multiplying the highest powers of all the primes:\[\] LCM = 2^3 \(\times\) 3^2 \(\times\) 5 \[\] \[\] Step 4: Calculate the product \[\] 1. (2^3 = 8) 2. (3^2 = 9) 3. Multiply these: (8 \(\times\) 9 = 72) 4. Now multiply (72 \(\times\) 5 = 360) \[\] \[\] Final Answer:\[\] The lowest common multiple of (24), (36), and (40) is (360). \[\] \[\] Correct Answer: (c)