Math worksheet for finding the least common multiple (LCM) of number sets.

Let's solve each of the Least Common Multiple (LCM) problems step by step. The LCM of a set of numbers is the smallest number that is a multiple of all the numbers in the set.

We’ll use the prime factorization method or division method to find the LCM.

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1. (20, 30, 40)

Already solved in the image:

We divide by common prime factors:

```
2 | 20 30 40
2 | 10 15 20
5 | 5 15 10
| 1 3 2
```

So:
- 20 = 2² × 5
- 30 = 2 × 3 × 5
- 40 = 2³ × 5

Take the highest powers of all primes:
- 2³ (from 40)
- 3¹ (from 30)
- 5¹ (common)

LCM = 2³ × 3 × 5 = 8 × 3 × 5 = 120

✔ Answer: 120

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2. (12, 18, 24)

Use division method:

```
2 | 12 18 24
3 | 6 9 12
| 2 3 4
```

Now we have:
- 2, 3, 4 → no more common divisors

So:
- 12 = 2² × 3
- 18 = 2 × 3²
- 24 = 2³ × 3

Highest powers:
- 2³ (from 24)
- 3² (from 18)

LCM = 2³ × 3² = 8 × 9 = 72

✔ Answer: 72

---

3. (6, 12, 30)

Prime factorization:
- 6 = 2 × 3
- 12 = 2² × 3
- 30 = 2 × 3 × 5

Highest powers:
- 2² (from 12)
- 3¹ (common)
- 5¹ (from 30)

LCM = 2² × 3 × 5 = 4 × 3 × 5 = 60

✔ Answer: 60

---

4. (5, 15, 25)

Factorize:
- 5 = 5
- 15 = 3 × 5
- 25 = 5²

Highest powers:
- 3¹ (from 15)
- 5² (from 25)

LCM = 3 × 5² = 3 × 25 = 75

✔ Answer: 75

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5. (20, 10, 25)

Factorize:
- 20 = 2² × 5
- 10 = 2 × 5
- 25 = 5²

Highest powers:
- 2² (from 20)
- 5² (from 25)

LCM = 2² × 5² = 4 × 25 = 100

✔ Answer: 100

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6. (25, 30, 35)

Factorize:
- 25 = 5²
- 30 = 2 × 3 × 5
- 35 = 5 × 7

Highest powers:
- 2¹ (from 30)
- 3¹ (from 30)
- 5² (from 25)
- 7¹ (from 35)

LCM = 2 × 3 × 5² × 7 = 2 × 3 × 25 × 7

Step-by-step:
- 2 × 3 = 6
- 6 × 25 = 150
- 150 × 7 = 1050

✔ Answer: 1050

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✔ Final Answers:

1. 120
2. 72
3. 60
4. 75
5. 100
6. 1050

Let me know if you'd like these shown with a visual diagram or explained using another method (like listing multiples).