There are several common methods to find the Least Common Multiple (LCM) of two or more numbers:
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Listing Multiples Method:
- List the first few multiples of each number.
- Identify the common multiples.
- The smallest common multiple is the LCM.
Example: For 4 and 5, multiples of 4 are 4, 8, 12, 16, 20..., multiples of 5 are 5, 10, 15, 20..., the LCM is 20.
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Prime Factorization Method:
- Find the prime factors of each number.
- Take each prime factor the maximum number of times it appears in any factorization.
- Multiply these prime factors to get the LCM.
Example: For 12 (2² × 3) and 30 (2 × 3 × 5), LCM = 2² × 3 × 5 = 60.
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Division Method (Ladder or Cake Method):
- Divide the numbers by common prime factors starting from the smallest prime.
- Continue dividing until all numbers become 1.
- Multiply all the prime divisors used to get the LCM.
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Using GCF (Greatest Common Factor):
- Use the formula LCM(a,b)=a×bGCF(a,b)\text{LCM}(a,b)=\frac{a\times b}{\text{GCF}(a,b)}LCM(a,b)=GCF(a,b)a×b.
