Finding LCM of 8, 12, and 20

The Least Common Multiple (LCM) is the smallest positive integer that is divisible by each of the given numbers.

Prime Factorization Method

We can find the LCM using the prime factorization method:

• Step 1: Find the prime factorization of each number.
  • $8 = 2 \times 2 \times 2 = 2^3$
  • $12 = 2 \times 2 \times 3 = 2^2 \times 3^1$
  • $20 = 2 \times 2 \times 5 = 2^2 \times 5^1$
• Step 2: Identify all the unique prime factors present in any of the factorizations.

  The unique prime factors are 2, 3, and 5.

• Step 3: Take the highest power of each unique prime factor.
  • Highest power of 2 is $2^3$.
  • Highest power of 3 is $3^1$.
  • Highest power of 5 is $5^1$.
• Step 4: Multiply these highest powers together to get the LCM.

  LCM = $2^3 \times 3^1 \times 5^1 = 8 \times 3 \times 5 = 120$.

Therefore, the LCM of 8, 12, and 20 is 120.