Find the LCM of the numbers given below :
16, 28, 40, 77

Answer

To find the LCM (Least Common Multiple) of the numbers 16, 28, 40, and 77, we can follow these steps:

### Step 1: Find the Prime Factorization of Each Number
- **16**: The prime factorization of 16 is \(2^4\) (since \(16 = 2 \times 2 \times 2 \times 2\)).
- **28**: The prime factorization of 28 is \(2^2 \times 7\) (since \(28 = 2 \times 2 \times 7\)).
- **40**: The prime factorization of 40 is \(2^3 \times 5\) (since \(40 = 2 \times 2 \times 2 \times 5\)).
- **77**: The prime factorization of 77 is \(7 \times 11\) (since \(77 = 7 \times 11\)).

### Step 2: Identify the Highest Power of Each Prime Factor
Now we need to take the highest power of each prime factor from the factorizations:
- For **2**, the highest power is \(2^4\) (from 16).
- For **5**, the highest power is \(5^1\) (from 40).
- For **7**, the highest power is \(7^1\) (from 28 and 77).
- For **11**, the highest power is \(11^1\) (from 77).

### Step 3: Multiply the Highest Powers Together
Now, we multiply these highest powers together to find the LCM:
\[ LCM = 2^4 \times 5^1 \times 7^1 \times 11^1 \]

Calculating this step-by-step:
1. \(2^4 = 16\)
2. \(5^1 = 5\)
3. \(7^1 = 7\)
4. \(11^1 = 11\)

Now multiply these together:
\[ LCM = 16 \times 5 \times 7 \times 11 \]

Calculating:
1. \(16 \times 5 = 80\)
2. \(80 \times 7 = 560\)
3. \(560 \times 11 = 6160\)

### Final Answer
Thus, the LCM of 16, 28, 40, and 77 is **6160**.

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