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## Finding the LCM Using Prime Factorization

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**Finding the LCM Using Prime Factorization**To determine the Least common Multiple: • Find the prime factorization for each number using exponents. • For each prime factor, write the base with the greatest exponent. • Multiply. Find the LCM of 36 and 24 36 24 /\ /\ 2 18 2 12 /\ /\ 2 9 2 6 /\ /\ 3 3 2 3 36= 2×2×3×3 24= 2×2×2×3 22 x 32 23 x 3 23 x 32 The LCM of 36 and 24 is 2X2X2X3X3 = 72**FINDING THE LCM USING PRIME FACTORIZATION**• Prime factor each number. Write using exponents. • For each prime factor, write the base with the greatest • exponent. • 3. Multiply all together. Find the GCF of 36 and 24 36 24 /\ /\ 2 18 2 12 /\ /\ 2 9 2 6 /\ /\ 3 3 2 3 36= 2×2×3×3 24= 2×2×2×3 22 x 32 23 x 3 22 x 3 The GCF of 36 and 24 is 2×2×3=12