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Ways to find LCM

  • Inspection - Solving a problem by looking at it and using logic, patterns, or quick mental math to see the answer, rather than a complex formula or step-by-step algorithm.
  • Prime Factorization
    1. Find the prime factors of each number.
    2. List all unique prime factors
    3. Select the one with the highest count or exponent.
    4. Multiply the selected prime factors together to get the LCM.
    5. An Example:
      • Prime Factors for 90 are: 23252\cdot 3^2 \cdot 5
      • Prime Factors for 12 are: 2232^2\cdot 3
      • The LCM is 22325=1802^2 \cdot 3^2 \cdot 5=180
  • Using Greatest Common Divisor
lcm(a,b)=abgcd(a,b)lcm(a,b)=\frac{|a\cdot b|}{gcd(a,b)}