LCM Via Prime Factorisation

• What is the first step in finding prime factors of a number?

  Find the prime factors of each number
• What does prime factorization involve?

  Writing each number as a product of its prime factors
• How do you find the prime factorization of 12, 18, and 24?

  • 12: $2^{2} \times 3$
  • 18: $2 \times 3^{2}$
  • 24: $2^{3} \times 3$
• What is the prime factorization of 12?

  $2^{2} \times 3$
• What is the prime factorization of 18?

  $2 \times 3^{2}$
• What is the prime factorization of 24?

  $2^{3} \times 3$
• How do you identify the highest power of each prime factor?

  Compare the powers of each prime in factorizations
• What are the highest powers of the prime factors 2 and 3 from the factorizations of 12, 18, and 24?

  • Prime factor 2: $2^{3}$
  • Prime factor 3: $3^{2}$
• What is the product of the highest powers of the prime factors 2 and 3?

  $72$
• How do you calculate the product of the highest powers of prime factors?

  Multiply the highest power of each prime factor
• What is the final product when multiplying the highest powers of 2 and 3?

  • Highest power of 2: $2^{3} =$$8$
  • Highest power of 3: $3^{2} =$$9$
  • Product: $2^{3} \times 3^{2} =$$72$