To find the least common multiple (LCM) of the given numbers, we need to determine the highest power of each prime factor that appears in any of the numbers and multiply them together.
The prime factors of the given numbers are:
2³ = 2 * 2 * 2
2² × 3 = 2 * 2 * 3
3² = 3 * 3
Now, we identify the highest power of each prime factor:
The highest power of 2 is 2³.
The highest power of 3 is 3².
To find the LCM, we multiply these highest powers together:
LCM = 2³ * 3² = 8 * 9 = 72.
Therefore, the LCM of 2³, 2²×3, and 3² is 72.