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To find the least common multiple (LCM) of 24, 40, and 72, first factorize each number into its prime factors: 24 = 2^3 * 3, 40 = 2^3 * 5, and 72 = 2^3 * 3^2. Then, identify the highest power of each prime factor that appears in any of the factorizations: 2^3, 3^2, and 5. Finally, multiply these highest powers together to find the LCM, which is 2^3 * 3^2 * 5 = 360.
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