4TH GRADE MATH - GREATEST COMMON FACTOR AND LEAST COMMON MULTIPLE ... - Free Printable

Let's solve each of these Greatest Common Factor (GCF) and Least Common Multiple (LCM) word problems step by step.

---

Problem 1:

Sara has 16 red flowers and 24 yellow flowers. She wants to make bouquets with the same number of each color flower in each bouquet. What is the greatest number of bouquets she can make?

#### Step 1: Understand the problem
We want to divide both 16 red and 24 yellow flowers into equal groups, with the same number of red and yellow flowers per bouquet. The goal is to make the greatest number of such bouquets.

This means we need the largest number that divides both 16 and 24 evenly — that’s the GCF.

#### Step 2: Find GCF of 16 and 24

- Factors of 16: 1, 2, 4, 8, 16
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- Common factors: 1, 2, 4, 8
- Greatest common factor = 8

So, Sara can make 8 bouquets.

#### Step 3: How many flowers per bouquet?
- Red flowers per bouquet: 16 ÷ 8 = 2
- Yellow flowers per bouquet: 24 ÷ 8 = 3

✔ Each bouquet has 2 red and 3 yellow flowers.

> ✔ Answer: 8 bouquets

---

Problem 2:

Two neon signs are turned on at the same time. Both signs blink as they are turned on. One sign blinks every 9 seconds. The other sign blinks every 15 seconds. In how many seconds will they blink together again?

#### Step 1: Understand the problem
We want to find when both signs blink at the same time again after starting together.

This is a Least Common Multiple (LCM) problem — we need the smallest number that is divisible by both 9 and 15.

#### Step 2: Find LCM of 9 and 15

Use prime factorization:

- 9 = 3²
- 15 = 3 × 5
- LCM = highest powers of all primes: 3² × 5 = 9 × 5 = 45

So, they will blink together again in 45 seconds.

> ✔ Answer: 45 seconds

---

Problem 3:

Lisa is making activity baskets to donate to charity. She has 12 coloring books, 28 markers, and 36 crayons. What is the greatest number of baskets she can make if each type of toy is equally distributed among the baskets? How many of each supply will go into the baskets?

#### Step 1: Understand the problem
We want to divide all items equally into baskets, with no leftovers, and make the maximum number of baskets possible.

So we need the GCF of 12, 28, and 36.

#### Step 2: Find GCF of 12, 28, and 36

- Prime factorization:
- 12 = 2² × 3
- 28 = 2² × 7
- 36 = 2² × 3²

Common prime factors: only 2² = 4

So, GCF = 4

She can make 4 baskets.

#### Step 3: How many of each item per basket?
- Coloring books: 12 ÷ 4 = 3 per basket
- Markers: 28 ÷ 4 = 7 per basket
- Crayons: 36 ÷ 4 = 9 per basket

> ✔ Answer:
> - Greatest number of baskets: 4
> - Per basket: 3 coloring books, 7 markers, 9 crayons

---

Problem 4:

The school cafeteria serves tacos every sixth day and cheeseburgers every eighth day. If tacos and cheeseburgers are both on today's menu, how many days will it be before they are both on the menu again?

#### Step 1: Understand the problem
They are both served today. We want to know when they will both appear again on the same day.

This is an LCM problem: find the least common multiple of 6 and 8.

#### Step 2: Find LCM of 6 and 8

- Prime factorization:
- 6 = 2 × 3
- 8 = 2³
- LCM = highest powers: 2³ × 3 = 8 × 3 = 24

So, in 24 days, both tacos and cheeseburgers will be on the menu again.

> ✔ Answer: 24 days

---

✔ Final Answers Summary:

1. 8 bouquets
2. 45 seconds
3. 4 baskets, each with 3 coloring books, 7 markers, and 9 crayons
4. 24 days

Let me know if you'd like a visual explanation or help with another problem!