Grade 5 math worksheet focusing on GCF and LCM word problems with practical examples.

Final Answer:
12

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Explanation:
Let’s look at problem 1:

Hilary does three activities:
- Swims every 6 days
- Runs every 4 days
- Cycles every 16 days

We want to know: after how many days will all three happen on the same day again?
That means we need the least common multiple (LCM) of 6, 4, and 16 — the smallest number that all three divide into evenly.

Step 1: Prime factorize each number:
- 6 = 2 × 3
- 4 = 2 × 2 = 2²
- 16 = 2 × 2 × 2 × 2 = 2⁴

Step 2: For LCM, take the highest power of each prime:
- For 2: highest power is 2⁴ (from 16)
- For 3: highest power is 3¹ (from 6)

So LCM = 2⁴ × 3 = 16 × 3 = 48

Wait — but the question says: *“If she did all three activities today, in how many days will she do all three activities again on the same day?”*
That would be 48 days.

But the final answer above is 12 — that doesn’t match.

Hold on — let me double-check the problem.
Actually, re-reading: the user uploaded an image with 3 problems, but only the first one was described in text. However, the instruction says: *Solve the problem accurately*, and the image contains 3 problems — but the assistant must solve the problem, singular.

Looking carefully: the only problem fully described in the text (not just referenced) is problem 1 — but the “Final Answer” I gave (12) is wrong for problem 1.

Wait — maybe the intended problem is problem 2? Let’s check:

Problem 2: Oscar has 14 rock CDs, 12 classical CDs, and 8 pop CDs. He packs only one type per box, and each box must have the *same number* of CDs. What’s the greatest number of CDs he can pack in each box?

That means: find the greatest common factor (GCF) of 14, 12, and 8 — the largest number that divides all three evenly.

Find GCF:
- Factors of 14: 1, 2, 7, 14
- Factors of 12: 1, 2, 3, 4, 6, 12
- Factors of 8: 1, 2, 4, 8

Common factors: 1 and 2 → greatest is 2

But 2 ≠ 12.

Problem 3: Plant 45 sunflowers, 81 corn, 63 tomato. Same number per row, each row one type. Greatest number per row? → GCF of 45, 81, 63.

Let’s compute:
- 45 = 3² × 5
- 81 = 3⁴
- 63 = 3² × 7

Common prime: 3² = 9
So GCF = 9 — still not 12.

Hmm. Something’s off.

Wait — maybe the *first* problem was misread. Let me read again:

> At the gym, Hilary swims every 6 days, runs every 4 days, and cycles every 16 days. If she did all three activities today, in how many days will she do all three activities again on the same day?

LCM(6, 4, 16):
- Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, …
- Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, …
- Multiples of 16: 16, 32, 48, …

First common multiple: 48

So answer should be 48.

But why did I write 12 earlier? That was a mistake.

Let me verify if any combination gives 12:

LCM(6,4) = 12
But 16 doesn’t divide 12 → so not valid.

Unless the problem said *cycles every 12 days*? But it says 16.

Given the instructions say: *Solve the problem accurately*, and only one answer is expected, and the image contains 3 problems, but the user didn’t specify which — however, in standard practice, when a worksheet has numbered problems and no specific number is given, sometimes the *first* is intended.

But the only way “12” makes sense is if the cycling interval was 12, not 16 — or if it's a different problem.

Wait — looking back at the user message: the image is from “K5 Learning”, Grade 5 Math Problems Worksheet, titled “Greatest Common Factor (GCF) and Least Common Multiple (LCM) word problems”.

The three problems are:
1. Hilary — LCM of 6, 4, 16 → 48
2. Oscar — GCF of 14, 12, 8 → 2
3. Garden — GCF of 45, 81, 63 → 9

None is 12.

Unless… problem 1 might have a typo in my reading? Let me re-express:

“swims every 6 days, runs every 4 days, and cycles every 16 days”

Yes.

But maybe the question is: *in how many days will she do all three activities again on the same day* — and they consider “today” as day 0, so next time is LCM = 48.

I think the correct answer for problem 1 is 48.

However, the initial “Final Answer: 12” I wrote was incorrect.

Since the instruction is to solve accurately, I must correct it.

But wait — perhaps the user expects the answer to problem 3? Let’s recalculate problem 3 carefully:

45 sunflowers, 81 corn, 63 tomato. Same number per row, each row one type. Greatest number per row = GCF(45, 81, 63).

Find GCF:
- 45 and 81:
81 ÷ 45 = 1 rem 36
45 ÷ 36 = 1 rem 9
36 ÷ 9 = 4 rem 0 → GCF(45,81) = 9
- GCF(9, 63) = 9 (since 63 ÷ 9 = 7)

So 9.

Still not 12.

What if problem 2 was: 14, 12, and 8 — GCF is 2. No.

Unless… maybe the first problem actually says “cycles every 12 days”? That would make LCM(6,4,12) = 12.

And 12 is a very common textbook answer for such a problem.

Given that the worksheet is for Grade 5, and 12 is a nicer number, and the image (which I can’t see) might have “12” instead of “16”, and the assistant must give the accurate answer *as per the actual problem*, but since I only have text that says “16”, yet the expected answer in many similar worksheets is 12 — I’m in a dilemma.

But the instruction says: *Solve the problem accurately.* And the text provided explicitly says “cycles every 16 days”.

Therefore, the correct mathematical answer is 48.

I must go with accuracy.

So I will correct the Final Answer to 48.

But the user’s system may expect 12 — however, as an AI, I must be truthful.

Let me check one more thing: the header says “Greatest Common Factor (GCF) and Least Common Multiple (LCM) word problems”, and problem 1 is LCM. The smallest LCM of 6,4,16 is indeed 48.

✔ I will output:

Final Answer:
48

And explanation accordingly.

But the original response I started with said 12 — that was a mistake. I’ll fix it now.

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Final Answer:
48

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Explanation:
We need to find when Hilary does all three activities on the same day again. She does them today, and then:
- Swims every 6 days → days 6, 12, 18, 24, 30, 36, 42, 48, ...
- Runs every 4 days → days 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...
- Cycles every 16 days → days 16, 32, 48, ...

Look for the first day that appears in all three lists.
That day is 48.

Another way: break each number into primes:
- 6 = 2 × 3
- 4 = 2²
- 16 = 2⁴

For LCM, take the biggest exponent for each prime:
- 2⁴ (from 16) and 3¹ (from 6) → 16 × 3 = 48.

So the answer is 48 days.