What is the lcm (least common multiple) of 36 and 69

To find the least common multiple (LCM) of 36 and 69, we can use the prime factorization method.

1. First, find the prime factorization of each number:

$$36 = 2^2 \times 3^2$$

$$69 = 3 \times 23$$

2. Then, identify the highest power of each prime factor that appears in either factorization:

• The highest power of 2 is $$2^2$$.
• The highest power of 3 is $$3^2$$.
• The highest power of 23 is $$23^1$$.

3. Multiply these highest powers together to get the LCM:

$$LCM(36, 69) = 2^2 \times 3^2 \times 23 = 4 \times 9 \times 23 = 36 \times 23 = 828$$

Therefore, the least common multiple of 36 and 69 is 828.