Question - Finding the Lowest Common Multiple

We need to find the LCM of 18, 36, and 54.

Step 1: Factor each number into its prime factors:

18 = 2 \times 3^2

36 = 2^2 \times 3^2

54 = 2 \times 3^3

Step 2: Take the highest power of each prime:

For 2: highest power is \(2^2\)

For 3: highest power is \(3^3\)

Step 3: Multiply these together:

LCM = 2^2 \times 3^3 = 4 \times 27 = 108

The lowest common multiple (LCM) of 18, 36, and 54 is 108.