The problem is to find the least common multiple (LCM) of 180 and 54.

1. Problem Description

The problem is to find the least common multiple (LCM) of 180 and

5

4.

2. Solution Steps

First, we find the prime factorization of 180 and

5

4.

$180 = 2^2 \times 3^2 \times 5$

$54 = 2 \times 3^3$

To find the LCM, we take the highest power of each prime factor that appears in either factorization.

LCM(a, b)

The prime factors involved are 2, 3, and

5.

The highest power of 2 is $2^2$.

The highest power of 3 is $3^3$.

The highest power of 5 is $5^1$.

Therefore, the LCM of 180 and 54 is $2^2 \times 3^3 \times 5$.

$LCM(180, 54) = 2^2 \times 3^3 \times 5 = 4 \times 27 \times 5 = 20 \times 27 = 540$.

3. Final Answer

$540$