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To find the least common multiple (LCM) of 30, 50, and 75, you first need to factorize each number into its prime factors. The prime factors of 30 are 2 x 3 x 5, the prime factors of 50 are 2 x 5^2, and the prime factors of 75 are 3 x 5^2. To find the LCM, you take the highest power of each prime factor that appears in any of the numbers, which gives you 2 x 3 x 5^2 = 150. Therefore, the LCM of 30, 50, and 75 is 150.
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