Factors, Multiples, GCF, and LCM
Warm-up
Divisibility rules quiz: is 312 divisible by 2? (Yes: ends in even digit.) By 3? (Yes: 3+1+2=6, divisible by 3.) By 6? (Yes: divisible by both 2 and 3.) By 4? (Yes: last two digits 12 are divisible by 4.) By 9? (No: 3+1+2=6, not divisible by 9.) Divisibility rules as a rapid-fire warm-up.
Explore
Factor investigation: each group receives 4 numbers (e.g., 36, 48, 72, 120). Build factor trees for each, find prime factorizations, use Venn diagrams to find GCF for pairs, and find LCMs. Challenge: what is the relationship between GCF, LCM, and the original numbers?
Consolidate
Practice
Students build prime factorizations for 6 numbers, find GCF and LCM for 4 pairs, and solve 2 fraction problems requiring GCF (simplification) and LCM (addition). Exit ticket: GCF of 18 and 30?
Exit ticket
Students build prime factorizations for 6 numbers, find GCF and LCM for 4 pairs, and solve 2 fraction problems requiring GCF (simplification) and LCM (addition). Exit ticket: GCF of 18 and 30?
84 = 2 x 42 = 2 x 2 x 21 = 2 x 2 x 3 x 7 = 2^2 x 3 x 7.
24 = 2^3 x 3. 36 = 2^2 x 3^2. GCF: min powers: 2^2 x 3 = 12. LCM: max powers: 2^3 x 3^2 = 72. Check: 12 x 72 = 864 = 24 x 36. Correct.