Find the LCM of 1, 4, 6, 12, 24, 36, and 54.
216
Express each number in terms of prime factors: \(4 = 2^2\), \(6 = 2 \times 3\), \(12 = 2^2 \times 3\), \(24 = 2^3 \times 3\), \(36 = 2^2 \times 3^2\), \(54 = 2 \times 3^3\).
The LCM takes the highest power of each prime present: \(2^3\) and \(3^3\).
So, \(\text{LCM} = 2^3 \times 3^3 = 8 \times 27 = 216\).
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