Math worksheet focusing on calculating the least common multiple (LCM) of three numbers.

Let's solve each of the Least Common Multiple (LCM) problems step by step.

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🔹 Problem 1: LCM of 36, 72, and 120

#### Step 1: Prime Factorization
- 36 = $ 2^2 \times 3^2 $
- 72 = $ 2^3 \times 3^2 $
- 120 = $ 2^3 \times 3 \times 5 $

#### Step 2: Take the highest power of each prime factor:
- $ 2^3 $ (from 72 and 120)
- $ 3^2 $ (from 36 and 72)
- $ 5^1 $ (from 120)

#### Step 3: Multiply them together:
$$
LCM = 2^3 \times 3^2 \times 5 = 8 \times 9 \times 5 = 360
$$

✔ LCM = 360

---

🔹 Problem 2: LCM of 46, 84, and 92

#### Step 1: Prime Factorization
- 46 = $ 2 \times 23 $
- 84 = $ 2^2 \times 3 \times 7 $
- 92 = $ 2^2 \times 23 $

#### Step 2: Highest powers of primes:
- $ 2^2 $ (from 84 and 92)
- $ 3^1 $ (from 84)
- $ 7^1 $ (from 84)
- $ 23^1 $ (from 46 and 92)

#### Step 3: Multiply:
$$
LCM = 2^2 \times 3 \times 7 \times 23 = 4 \times 3 \times 7 \times 23
$$
Break it down:
- $ 4 \times 3 = 12 $
- $ 12 \times 7 = 84 $
- $ 84 \times 23 = 1932 $

✔ LCM = 1932

---

🔹 Problem 3: LCM of 47, 72, and 16

#### Step 1: Prime Factorization
- 47 = $ 47 $ → it's a prime number
- 72 = $ 2^3 \times 3^2 $
- 16 = $ 2^4 $

#### Step 2: Highest powers:
- $ 2^4 $ (from 16)
- $ 3^2 $ (from 72)
- $ 47^1 $ (from 47)

#### Step 3: Multiply:
$$
LCM = 2^4 \times 3^2 \times 47 = 16 \times 9 \times 47
$$
- $ 16 \times 9 = 144 $
- $ 144 \times 47 $

Now compute:
$$
144 \times 47 = 144 \times (50 - 3) = 144 \times 50 - 144 \times 3 = 7200 - 432 = 6768
$$

✔ LCM = 6768

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✔ Final Answers:

1. LCM of (36, 72, 120) = 360
2. LCM of (46, 84, 92) = 1932
3. LCM of (47, 72, 16) = 6768

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You can fill in the worksheet as follows:

```
L.C.M of (36, 72 and 120) L.C.M of (46, 84 and 92) L.C.M of (47, 72 and 16)
36 72 120 46 84 92 47 72 16


L.C.M = 360 L.C.M = 1932 L.C.M = 6768
```

Let me know if you'd like a visual explanation or method using the ladder method!