The least common multiple (L.C.M.) of two numbers is the smallest positive integer that is perfectly divisible by the two given numbers.
For example, the L.C.M. of 12 and 14 is 84.
Program to Compute LCM
# Python Program to find the L.C.M. of two input number def compute_lcm(x, y): # choose the greater number if x > y: greater = x else: greater = y while(True): if((greater % x == 0) and (greater % y == 0)): lcm = greater break greater += 1 return lcm num1 = 54 num2 = 24 print("The L.C.M. is", compute_lcm(num1, num2))
The L.C.M. is 216
Note: To test this program, change the values of
This program stores two number in
num2 respectively. These numbers are passed to the
compute_lcm() function. The function returns the L.C.M of two numbers.
In the function, we first determine the greater of the two numbers since the L.C.M. can only be greater than or equal to the largest number. We then use an infinite
while loop to go from that number and beyond.
In each iteration, we check if both the numbers perfectly divide our number. If so, we store the number as L.C.M. and break from the loop. Otherwise, the number is incremented by 1 and the loop continues.
The above program is slower to run. We can make it more efficient by using the fact that the product of two numbers is equal to the product of the least common multiple and greatest common divisor of those two numbers.
Number1 * Number2 = L.C.M. * G.C.D.
Here is a Python program to implement this.
Program to Compute LCM Using GCD
# Python program to find the L.C.M. of two input number # This function computes GCD def compute_gcd(x, y): while(y): x, y = y, x % y return x # This function computes LCM def compute_lcm(x, y): lcm = (x*y)//compute_gcd(x,y) return lcm num1 = 54 num2 = 24 print("The L.C.M. is", compute_lcm(num1, num2))
The output of this program is the same as before. We have two functions
compute_lcm(). We require G.C.D. of the numbers to calculate its L.C.M.
compute_lcm() calls the function
compute_gcd() to accomplish this. G.C.D. of two numbers can be calculated efficiently using the Euclidean algorithm.
Click here to learn more about methods to calculate G.C.D in Python.