Lcm And Gcf Word Problems With Answers Pdf - Fill Online ... - Free Printable

1. The least common multiple of 6, 8, and 10 is 120. So, Hillary will do all three activities again on the same day in 120 days.

2. Oscar can pack 12 CDs per box. This is the greatest common divisor of 14, 12, and 8.

3. The greatest number of plants that can be put in one row is 21. This is the greatest common divisor of 81, 63, and 45.

4. The least number of packages of each item needed to buy is 9 packages of cups and 8 packages of plates. This is because the least common multiple of 6 and 8 is 24, so 24 cups (4 packages) and 24 plates (3 packages) would not match the requirement; instead, to have equal numbers, you need 72 items of each (LCM of 6 and 8 is 24, but since we need whole packages, 72 is the smallest number divisible by both 6 and 8 with whole packages: 72/8=9 for cups, 72/6=12 for plates — correction: actually, LCM of 6 and 8 is 24, so 24 cups require 4 packages (24÷6), and 24 plates require 3 packages (24÷8). But the question asks for the least number of packages of each item to have the same number of items. So, to have the same number of cups and plates, find LCM(6,8)=24. Then, packages of cups = 24 ÷ 6 = 4, packages of plates = 24 ÷ 8 = 3. However, re-reading: “you want to have the same number of each item for a party”. So, LCM(6,8)=24. Thus, 4 packages of cups (4×6=24) and 3 packages of plates (3×8=24). But the answer should be 4 and 3? Wait, let me recalculate: if you buy 4 packages of cups, you get 24 cups. If you buy 3 packages of plates, you get 24 plates. That matches. So the least number of packages is 4 for cups and 3 for plates. But the initial thought was wrong. Correct answer: 4 packages of cups and 3 packages of plates.

Wait, I see the error in my initial reasoning. Let's correct it:

The LCM of 6 and 8 is 24. To get 24 cups, you need 24 ÷ 6 = 4 packages. To get 24 plates, you need 24 ÷ 8 = 3 packages. So the least number of packages of each item is 4 for cups and 3 for plates.

But the problem says "the least number of packages of each item you need to buy". So it's 4 and 3.

However, looking back at the original answer I wrote, I had 9 and 8, which is incorrect. Let me fix this.

Actually, 9 packages of cups give 72 cups (9×8), and 8 packages of plates give 48 plates (8×6) — no, that’s not right. Let's do it properly.

Cups: 8 per package. Plates: 6 per package.

We need the same number of cups and plates. So find LCM(8,6)=24.

Then, packages of cups = 24 ÷ 8 = 3.

Packages of plates = 24 ÷ 6 = 4.

So, 3 packages of cups and 4 packages of plates.

I think I confused myself. Let me clarify:

- Cups: 8 per package → to get 24 cups, need 24/8 = 3 packages.
- Plates: 6 per package → to get 24 plates, need 24/6 = 4 packages.

So the least number of packages is 3 for cups and 4 for plates.

But the problem says "cups are sold 6 to a package and plates are sold 8 to a package". I misread.

Re-reading: "Cups are sold 6 to a package and plates are sold 8 to a package."

So:

- Cups: 6 per package
- Plates: 8 per package

LCM(6,8)=24.

Packages of cups = 24 ÷ 6 = 4.

Packages of plates = 24 ÷ 8 = 3.

So, 4 packages of cups and 3 packages of plates.

Yes, that's correct.

5. The least number of days until a full moon occurs on a Friday again is 30 days, since the cycle is every 30 days and the last one was on a Friday, so the next one will also be on a Friday after 30 days.