1Cademy - Finding the LCM of 12 and 18 Using Prime Factors

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Finding the LCM of 12 and 18 Using Prime Factors

Find the least common multiple (LCM) of $12$ and $18$ using the Prime Factors Method. Step 1. Write each as a product of primes: $12 = 2 \cdot 2 \cdot 3$ and $18 = 2 \cdot 3 \cdot 3$ . Step 2. List the primes and match them vertically in columns: $12 = 2 \cdot 2 \cdot 3$ $18 = 2 \cdot \quad 3 \cdot 3$ Step 3. Bring down one prime factor from each column to get $2$ , $2$ , $3$ , and $3$ . Step 4. Multiply these factors together: $ext{LCM} = 2 \cdot 2 \cdot 3 \cdot 3 = 36$ . The prime factors of $12$ ( $2 \cdot 2 \cdot 3$ ) and the prime factors of $18$ ( $2 \cdot 3 \cdot 3$ ) are all included in the LCM ( $2 \cdot 2 \cdot 3 \cdot 3$ ). By matching up the common primes, each shared prime factor is used only once, ensuring $36$ is the least common multiple.