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To find the least common multiple (LCM) of 48, 84, and 144, we first need to find the prime factorization of each number.
48 = 2^4 * 3 84 = 2^2 * 3 * 7 144 = 2^4 * 3^2
Next, we take the highest power of each prime factor that appears in any of the numbers: 2^4, 3^2, 7.
Multiplying these together, we get LCM(48, 84, 144) = 2^4 * 3^2 * 7 = 2016.
Therefore, the least common multiple of 48, 84, and 144 is 2016.
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