Least Common Multiple (LCM) Worksheet | 6th Grade PDF Worksheets - Free Printable

Let's solve this step by step, working through each section of the worksheet.

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Section A: Circle the numbers that are multiples of both numbers in the first column.

We are to find common multiples of the two numbers listed in each row.

#### Row 1: 2 and 5
Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, ...
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, ...

Common multiples: 10, 20, 30, 40, 50, 60, ...

From the list:
8, 10, 12, 15, 25, 30, 45, 60, 100

Numbers divisible by both 2 and 5 → must be divisible by 10 (since LCM of 2 and 5 is 10).

So circle: 10, 30, 60, 100

✔ Already done: 10 is circled.

So we need to circle: 30, 60, 100

> ✔ Final answer for Row 1: 10, 30, 60, 100

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#### Row 2: 3 and 4
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...

Common multiples: 12, 24, 36, 48, ...

List given: 6, 8, 12, 16, 21, 24, 30, 36, 96

Check which are divisible by both 3 and 4:

- 6 → divisible by 3, not by 4 ✘
- 8 → divisible by 4, not by 3 ✘
- 12 → yes ✔
- 16 → no ✘
- 21 → no ✘
- 24 → yes ✔
- 30 → no ✘
- 36 → yes ✔
- 96 → yes ✔

So circle: 12, 24, 36, 96

✔ Answer: 12, 24, 36, 96

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#### Row 3: 6 and 8
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ...

Common multiples: 24, 48, 72, ...

Given list: 8, 12, 16, 24, 40, 72, 480, 600, 800

Check:

- 8 → multiple of 8, but not 6 ✘
- 12 → multiple of 6, not 8 ✘
- 16 → multiple of 8, not 6 ✘
- 24 → yes ✔
- 40 → multiple of 8? yes; 6? 40 ÷ 6 = 6.66… ✘
- 72 → yes ✔
- 480 → 480 ÷ 6 = 80, 480 ÷ 8 = 60 → yes ✔
- 600 → 600 ÷ 6 = 100, 600 ÷ 8 = 75 → yes ✔
- 800 → 800 ÷ 6 ≈ 133.33 → no ✘

So circle: 24, 72, 480, 600

✔ Answer: 24, 72, 480, 600

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Section B: Write the first ten multiples of each number

#### 4:
Already started: 4, 8, 12
Next: 16, 20, 24, 28, 32, 36, 40

→ 4, 8, 12, 16, 20, 24, 28, 32, 36, 40

#### 5:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50

→ 5, 10, 15, 20, 25, 30, 35, 40, 45, 50

#### 9:
9, 18, 27, 36, 45, 54, 63, 72, 81, 90

→ 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

#### 12:
12, 24, 36, 48, 60, 72, 84, 96, 108, 120

→ 12, 24, 36, 48, 60, 72, 84, 96, 108, 120

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Use the table above to identify the following:

#### a) The LCM of 4 and 5

Look at multiples of 4: 4, 8, 12, 16, 20, 24, ...
Multiples of 5: 5, 10, 15, 20, 25, ...

First common multiple: 20

✔ LCM = 20

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#### b) The LCM of 4, 8, and 12

Find smallest number that appears in all three lists.

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, ...
Multiples of 8: 8, 16, 24, 32, 40, 48, ...
Multiples of 12: 12, 24, 36, 48, ...

Common multiples: 24, 48, ...

Smallest: 24

✔ LCM = 24

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#### c) The LCM of 9 and 12

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, ...

Common: 36, 72, ...

Smallest: 36

✔ LCM = 36

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#### d) The LCM of 5, 12, and 15

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, ...
Multiples of 15: 15, 30, 45, 60, 75, ...

Common: 60, 120, ...

Smallest: 60

✔ LCM = 60

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Section C: Word Problems

#### 1) Train A stops every 9 minutes. Train B stops every 15 minutes. If they start at the same time, how long until they stop at the same time again?

We need the LCM of 9 and 15.

Prime factorization:
- 9 = 3²
- 15 = 3 × 5

LCM = 3² × 5 = 9 × 5 = 45

✔ So they will stop together again after 45 minutes.

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#### 2) Cameron collects snails every 3 days and shells every 16 days. On Wednesday he does both. When next?

Need LCM of 3 and 16

- 3 is prime
- 16 = 2⁴

No common factors → LCM = 3 × 16 = 48

So every 48 days he does both.

He did it on Wednesday, so add 48 days.

Now count forward 48 days from Wednesday.

- 48 ÷ 7 = 6 weeks and 6 days
- 6 weeks = 42 days → back to Wednesday
- Add 6 more days: Wednesday → Thursday → Friday → Saturday → Sunday → Monday → Tuesday

Wait: 42 days = exactly 6 weeks → still Wednesday

Then 48 days = 42 + 6 → Saturday

✔ So next day he collects both is Saturday

But wait — let’s double-check:

- Start: Wednesday
- After 48 days: 48 mod 7 = 6 → 6 days after Wednesday → Tuesday?

Wait! Let's do it properly:

Days of week cycle every 7.

48 ÷ 7 = 6 remainder 6

So 6 days after Wednesday:

- Day 1: Thursday
- Day 2: Friday
- Day 3: Saturday
- Day 4: Sunday
- Day 5: Monday
- Day 6: Tuesday

✔ So 48 days later is Tuesday

Answer: Tuesday

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#### 3) Eggs come in packs of 9. Bread comes in packs of 24. She wants one egg per slice of bread. How many packs of each should she buy?

She needs equal number of eggs and slices of bread.

So find LCM of 9 and 24 → smallest number divisible by both.

Prime factorization:
- 9 = 3²
- 24 = 2³ × 3

LCM = 2³ × 3² = 8 × 9 = 72

So she needs 72 eggs and 72 slices of bread

Now:
- Packs of eggs: 72 ÷ 9 = 8 packs
- Packs of bread: 72 ÷ 24 = 3 packs

✔ She should buy 8 packs of eggs and 3 packs of bread

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✔ Final Answers Summary

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Section A: Circle common multiples

- 2 and 5: 10, 30, 60, 100
- 3 and 4: 12, 24, 36, 96
- 6 and 8: 24, 72, 480, 600

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Section B: First 10 multiples

| Number | Multiples |
|--------|-----------|
| 4 | 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 |
| 5 | 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 |
| 9 | 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 |
| 12 | 12, 24, 36, 48, 60, 72, 84, 96, 108, 120 |

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Section B: Identify LCMs

a) LCM of 4 and 5 → 20
b) LCM of 4, 8, 12 → 24
c) LCM of 9 and 12 → 36
d) LCM of 5, 12, 15 → 60

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Section C: Word Problems

1) Trains stop together again after 45 minutes
2) Next day he collects both: Tuesday
3) Buy 8 packs of eggs and 3 packs of bread

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