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Finding the LCM & GCF LCM {Least Common Multiple} GCF {Greatest Common Factor} Use to find common denominator Use to reduce fractions Find the LCM for 24, 36, and 50 Find the GCF for 126 and 180 Step 1: Find the Prime Factorization of each number Step 1: Find the Prime Factorization of both numbers 24 36 50 9 3 3 1 1 90 63 25 45 21 5 15 7 1 5 1 Step 2: Place the Prime Factors in a Box 24 36 50 0 8 1 2 2 3 3 5 6 180 6 2 1 2 3 3 7 18 0 5 2 5 5 6 3 2 2 3 3 4 2 2 2 2 3 12 126 2 3 2·2·2 2·2 2 3 3·3 Step 2: 1 Place the Prime factors in a Box 5 126 180 2 3 2 2·2 3·3 3·3 5 7 7 5 5·5 Step 3: Circle the greatest amount of times each prime factor occurs, Step 3: Circle the least amount of times each prime factor occurs, even if the factor is not common to all three numbers. But the factors must be common to both numbers! Note: 24 and 35 do not have 5 as a common factor, but 50 does so, we circle the 5’s also. Saved: San Eil (Math Handout) LCM-GCF & EPCC (Math Emporium) HANDOUT LCM-GCF So, do not use (5) or (7) because they are not common to both 126 and 180 1