don't want answer from chat gpt. ### Recursive Function for Calculating Least Common Multiple (LCM)In this exercise, we aim to develop a recursive function `lcm` that:1. **Takes Two Unsigned Integers as Input** - The function will accept two unsigned integers, `a` and `b`, as its arguments.2. **Returns an Unsigned Integer as Output** - The function will return an unsigned integer `z`, which represents the least common multiple (LCM) of `a` and `b`.3. **Error Handling** - The function includes basic error checking to ensure it operates correctly or throws appropriate exceptions if necessary.#### Definition of Least Common Multiple (LCM)The least common multiple (LCM) of two integers `a` and `b` is the smallest positive integer `z` that is divisible by both `a` and `b` without leaving any remainder.### Function DesignHere's the pseudocode for the recursive `lcm` function:```pythondef gcd(a, b): if b == 0: return a else: return gcd(b, a % b)def lcm(a, b): if a == 0 or b == 0: raise ValueError("Inputs must be non-zero.") return (a * b) // gcd(a, b)```### Explanation1. **GCD Sub-function**: - The `gcd` function calculates the greatest common divisor (GCD) using a recursive approach based on the Euclidean algorithm.2. **LCM Calculation**: - The `lcm` function computes the LCM using the relationship between GCD and LCM: \[ \text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)} \] - It performs a check to ensure that neither `a` nor `b` are zero before proceeding.### Test CasesUtilize the function to compute the LCM for the following pairs:1. **Case (i)**: - Inputs: `a = 97`, `b = 311` - Output: \[ \text{LCM}(97, 311) = 30167 \]2. **Case (ii)**: - Inputs: `a = 77777`, `b = 678

As the programming language is not mentioned here we are using C programmingIn C, the maximum value…

Write (on paper) the code for a RECURSIVE function called 'Icm' that: a. Takes two unsigned integers a and b as input, b. Returns an unsigned integer z as output which will be the least common multiple of a and b, c. Does any error checking or throws any exception as may be needed. A least common multiple z is the lowest number which can be fully divided by both inputs a and b without leaving a remainder. Then write the output of your function for the following two cases: (i) a = 97, b = 311 (ii) a = 77777, b = 67890

Write (on paper) the code for a RECURSIVE function called 'Icm' that: a. Takes two unsigned integers a and b as input, b. Returns an unsigned integer z as output which will be the least common multiple of a and b, c. Does any error checking or throws any exception as may be needed. A least common multiple z is the lowest number which can be fully divided by both inputs a and b without leaving a remainder. Then write the output of your function for the following two cases: (i) a = 97, b = 311 (ii) a = 77777, b = 67890

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Chapter1: Introduction

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don't want answer from chat gpt.

### Recursive Function for Calculating Least Common Multiple (LCM)

In this exercise, we aim to develop a recursive function `lcm` that:

1. **Takes Two Unsigned Integers as Input**
- The function will accept two unsigned integers, `a` and `b`, as its arguments.

2. **Returns an Unsigned Integer as Output**
- The function will return an unsigned integer `z`, which represents the least common multiple (LCM) of `a` and `b`.

3. **Error Handling**
- The function includes basic error checking to ensure it operates correctly or throws appropriate exceptions if necessary.

#### Definition of Least Common Multiple (LCM)
The least common multiple (LCM) of two integers `a` and `b` is the smallest positive integer `z` that is divisible by both `a` and `b` without leaving any remainder.

### Function Design
Here's the pseudocode for the recursive `lcm` function:

```python
def gcd(a, b):
if b == 0:
return a
else:
return gcd(b, a % b)

def lcm(a, b):
if a == 0 or b == 0:
raise ValueError("Inputs must be non-zero.")
return (a * b) // gcd(a, b)
```

### Explanation
1. **GCD Sub-function**:
- The `gcd` function calculates the greatest common divisor (GCD) using a recursive approach based on the Euclidean algorithm.

2. **LCM Calculation**:
- The `lcm` function computes the LCM using the relationship between GCD and LCM:
\[
\text{LCM}(a, b) = \frac{a \times b}{\text{GCD}(a, b)}
\]
- It performs a check to ensure that neither `a` nor `b` are zero before proceeding.

### Test Cases
Utilize the function to compute the LCM for the following pairs:

1. **Case (i)**:
- Inputs: `a = 97`, `b = 311`
- Output:
\[
\text{LCM}(97, 311) = 30167
\]

2. **Case (ii)**:
- Inputs: `a = 77777`, `b = 678

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