Question

and multiples
(gcf and lcm)

• gcf (greatest common factor): list the factors (numbers that divide evenly). pick the biggest match. used for splitting things into equal groups.
• lcm (least common multiple): skip count (3, 6, 9...). pick the first match. used for when two events will happen at the same time again.

practice problems:

1. find the greatest common factor (gcf) of 12 and 18.
2. find the least common multiple (lcm) of 4 and 8.
3. bree is planning a party. she wants to make gift bags for her guests.

a. she has 24 stickers and 36 pieces of candy. she wants to divide them evenly into the gift bags with no leftovers. what is the greatest number of gifts she can make?
b. bree also wants to buy plates and napkins. plates come in packs of 8. napkins come in packs of 12. what is the least number of packs of each she must buy to have an equal number of plates and napkins?
packs of plates: __________
packs of napkins: __________

Explanation:

Problem 5: Find the GCF of 12 and 18

Step 1: List factors of 12

Factors of 12: \(1, 2, 3, 4, 6, 12\)

Step 2: List factors of 18

Factors of 18: \(1, 2, 3, 6, 9, 18\)

Step 3: Identify common factors

Common factors: \(1, 2, 3, 6\)

Step 4: Pick the largest common factor

Largest common factor is \(6\)

Step 1: List multiples of 4

Multiples of 4: \(4, 8, 12, 16, \dots\)

Step 2: List multiples of 8

Multiples of 8: \(8, 16, 24, \dots\)

Step 3: Identify the first common multiple

First common multiple is \(8\)

Step 1: Identify numbers to find GCF of

We need GCF of 24 (stickers) and 36 (candy)

Step 2: List factors of 24

Factors of 24: \(1, 2, 3, 4, 6, 8, 12, 24\)

Step 3: List factors of 36

Factors of 36: \(1, 2, 3, 4, 6, 9, 12, 18, 36\)

Step 4: Identify common factors

Common factors: \(1, 2, 3, 4, 6, 12\)

Step 5: Pick the largest common factor

Largest common factor is \(12\)

Answer:

\(6\)

Problem 6: Find the LCM of 4 and 8