Sure, here is a Python function that calculates the LCM and GCD of two numbers:

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

def lcm(a, b):
return (a / gcd(a, b)) * b

def lcmAndGcd(a, b):
return [lcm(a, b), gcd(a, b)]
```

Here's how it works:

1. The `gcd` function uses the Euclidean algorithm to find the greatest common divisor of `a` and `b`. If `a` is 0, it returns `b`. Otherwise, it recursively calls itself with `b % a` and `a`.

2. The `lcm` function calculates the least common multiple of `a` and `b` by dividing `a` by their GCD and then multiplying by `b`. This works because `a * b = lcm(a, b) * gcd(a, b)`.

3. The `lcmAndGcd` function returns a list containing the LCM and GCD of `a` and `b`.

The time complexity of this function is O(log(min(a, b))) because the Euclidean algorithm runs in logarithmic time. The auxiliary space complexity is O(1) because it uses a constant amount of space.

Question

Sure, here is a Python function that calculates the LCM and GCD of two numbers:

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

def lcm(a, b):
    return (a / gcd(a, b)) * b

def lcmAndGcd(a, b):
    return [lcm(a, b), gcd(a, b)]
```

Here's how it works:

1. The `gcd` function uses the Euclidean algorithm to find the greatest common divisor of `a` and `b`. If `a` is 0, it returns `b`. Otherwise, it recursively calls itself with `b % a` and `a`.

2. The `lcm` function calculates the least common multiple of `a` and `b` by dividing `a` by their GCD and then multiplying by `b`. This works because `a * b = lcm(a, b) * gcd(a, b)`.

3. The `lcmAndGcd` function returns a list containing the LCM and GCD of `a` and `b`.

The time complexity of this function is O(log(min(a, b))) because the Euclidean algorithm runs in logarithmic time. The auxiliary space complexity is O(1) because it uses a constant amount of space.

Knowee AI · Accepted Answer

Sure, here is a Python function that calculates the LCM and GCD of two numbers:

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

def lcm(a, b):
    return (a / gcd(a, b)) * b

def lcmAndGcd(a, b):
    return [lcm(a, b), gcd(a, b)]
```

Here's how it works:

1. The `gcd` function uses the Euclidean algorithm to find the greatest common divisor of `a` and `b`. If `a` is 0, it returns `b`. Otherwise, it recursively calls itself with `b % a` and `a`.

2. The `lcm` function calculates the least common multiple of `a` and `b` by dividing `a` by their GCD and then multiplying by `b`. This works because `a * b = lcm(a, b) * gcd(a, b)`.

3. The `lcmAndGcd` function returns a list containing the LCM and GCD of `a` and `b`.

The time complexity of this function is O(log(min(a, b))) because the Euclidean algorithm runs in logarithmic time. The auxiliary space complexity is O(1) because it uses a constant amount of space.

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