8) amy is buying cups and plates for a party. the cups come in packs of 4 and plates come in packs of 6. she…

8) amy is buying cups and plates for a party. the cups come in packs of 4 and plates come in packs of 6. she wants to purchase the fewest cups and plates possible, but wants to have the same number of each. how many cups and plates does she need to buy?

8) amy is buying cups and plates for a party. the cups come in packs of 4 and plates come in packs of 6. she wants to purchase the fewest cups and plates possible, but wants to have the same number of each. how many cups and plates does she need to buy?

Answer

Explanation:

Step1: Find LCM of 4 and 6

Prime factors of 4: $4 = 2\times2$
Prime factors of 6: $6 = 2\times3$
LCM is product of highest powers: $2^2\times3 = 12$

Step2: Verify number of packs

Cups: $\frac{12}{4} = 3$ packs
Plates: $\frac{12}{6} = 2$ packs

Answer:

Amy needs to buy 12 cups and 12 plates.