This code snippet defines two functions: one to calculate the Greatest Common Divisor (GCD) using the Euclidean algorithm and another to calculate the Least Common Multiple (LCM) using the GCD.

```
def gcd(a, b):
if a == 0:
return b
elif b == 0:
return a
elif a > b:
return gcd(a - b, b)
else:
return gcd(a, b - a)
def lcm(a, b):
return a * b / gcd(a, b)
a, b = 20, 8
print("Least common multiple is: " + str(lcm(a, b)))
```

`Least common multiple is: 40.0`

`gcd(a, b)`

```
def gcd(a, b):
if a == 0:
return b
elif b == 0:
return a
elif a > b:
return gcd(a - b, b)
else:
return gcd(a, b - a)
```

**Purpose**: This function calculates the GCD of two integers`a`

and`b`

.**Parameters**: The function takes two parameters:`a`

: The first integer.`b`

: The second integer.

**Base Cases**:`if a == 0`

: If`a`

is 0, the GCD is`b`

. This is because the GCD of 0 and any number`b`

is`b`

.`elif b == 0`

: If`b`

is 0, the GCD is`a`

. Similarly, the GCD of 0 and any number`a`

is`a`

.

**Recursive Cases**:`elif a > b`

: If`a`

is greater than`b`

, the function calls itself with`a - b`

and`b`

. This step reduces the value of`a`

by subtracting`b`

from it.`else`

: If`b`

is greater than or equal to`a`

, the function calls itself with`a`

and`b - a`

. This step reduces the value of`b`

by subtracting`a`

from it.

This process continues recursively until one of the base cases is met, effectively reducing the problem size at each step.

`lcm(a, b)`

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

**Purpose**: This function calculates the Least Common Multiple (LCM) of two integers`a`

and`b`

.**Parameters**: The function takes two parameters:`a`

: The first integer.`b`

: The second integer.

**Calculation**:- The function uses the formula LCM(a,b)=a×bGCD(a,b)LCM(a,b)=GCD(a,b)a×b.
- It multiplies
`a`

and`b`

and then divides the product by the GCD of`a`

and`b`

, which is calculated using the`gcd`

function.

`a, b = 20, 8`

**Variable Initialization**: Two variables`a`

and`b`

are initialized with the values`20`

and`8`

respectively.

`print("Least common multiple is: " + str(lcm(a, b)))`

**Function Call and Output**:- The
`lcm`

function is called with`a`

and`b`

as arguments. - The result, which is the LCM of
`20`

and`8`

, is converted to a string and concatenated with the message “Least common multiple is: “. - This message is printed to the console.

- The

For `lcm(20, 8)`

, the function will perform the following steps:

**Calculate GCD**:`gcd(20, 8)`

`20 > 8`

, so it calls`gcd(20 - 8, 8)`

which is`gcd(12, 8)`

.`12 > 8`

, so it calls`gcd(12 - 8, 8)`

which is`gcd(4, 8)`

.`4 < 8`

, so it calls`gcd(4, 8 - 4)`

which is`gcd(4, 4)`

.`4 == 4`

, so it calls`gcd(4, 4 - 4)`

which is`gcd(4, 0)`

.- Since
`b == 0`

, it returns`4`

.

**Calculate LCM**:`lcm(20, 8)`

- Using the formula LCM(20,8)=20×8 /GCD(20,8)
- Substituting the values: LCM(20,8)=20×8/4=40

Login

Accessing this tutorial requires a login. Please enter your credentials below!