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To find the least common multiple (LCM) of 45, 54, and 72, we first need to find the prime factorization of each number. The prime factorization of 45 is 3^2 * 5, 54 is 2 * 3^3, and 72 is 2^3 * 3^2. Then, we take the highest power of each prime factor that appears in any of the numbers: 2^3 * 3^3 * 5 = 540. Therefore, the LCM of 45, 54, and 72 is 540.
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