CODEWITHSUNDEEP
pythonfor-loopmathwhile-loopbreak
KillingSpree
KillingSpree

Reputation: 101

How to find the lowest number that is divisible by two other numbers?

The requirement for my program is:

Complete the following program so that the loop stops when it has found the smallest positive integer greater than 1000 that is divisible by both 33 and 273.

This is my code that I have tried so far:

n = 1001 #This one is required

while True: #This one too
    for i in range(n,___): # I don't know what should i put in the blank
          if i%33 == 0 and i%273 == 0: # I really confused about this line
              break # Should i break it now?, or in the other lines?
print(f"The value of n is {n}") #This one is also required

I have tried to use the break under for-statement but nothing returns. I don't know where I should put a break, in which lines or if I even need it at all.

How should I write the loops to get the correct result?

Upvotes: 5

Views: 388

Answers (5)

Kemal
Kemal

Reputation: 19

Use the Least Common Multiple (LCM) of 33 and 273:

import math

# Get user input
num1 = int(input("Enter the first number: "))
num2 = int(input("Enter the second number: "))
sn = int(input("Enter the starting number (must be greater than 0): "))

# Find the LCM of the two numbers
lcm = math.lcm(num1, num2)

# Find the smallest multiple of LCM greater than sn-1
n = sn if sn % lcm == 0 else ((sn // lcm) + 1) * lcm

print(f"The smallest number greater than {sn-1} that is divisible by {num1} and {num2} is {n}")

The output:

Enter the first number: 33
Enter the second number: 273
Enter the starting number (must be greater than 0): 1001
The smallest number greater than 1000 that is divisible by 33 and 273 is 3003

Upvotes: 0

Deepstop
Deepstop

Reputation: 3817

Well you could still use a for loop, as long as the upper limit is at least as high as the maximum possible result. The result would be in i, not in n, and the for loop will suffice, not an additional while loop. The for loop will break when the remainder when dividing by both 33 and 237 is zero (i.e. they are both factors).

n = 1001

for i in range(n, 33 * 237 + 1): 
    if i % 33 == 0 and i % 237 == 0:
        break
print(f"The value of i is {i}")

You could also use a while loop and use the same logic for the condition. In this case we test that at least one is not a factor and continue the loop until both 33 and 237 are evenly divisible into i.

n = 1001

i = n
while i % 33 or i % 237:
    i += 1
print(f"The value of i is {i}")

Upvotes: 1

Ian McGowan
Ian McGowan

Reputation: 3799

There are few things to explain:

  1. n%33 is the remainder of dividing n by 33. So 66%33 is 0 and 67%33 is 1.

  2. For loops are generally when you need to loop over a defined range (not always, but usually). E.g. "add up the first 100 integers". A while loop makes more sense here. It will definitely terminate, because at some point you'll get to 33 * 237.

  3. if i%33 == 0 and i%237 == 0: means we want to do something when the number can be divided evenly (no remainder) by both 37 and 237.

    n=1001 while True: if n%33==0 and n%237==0: print(n) break n+=1

Upvotes: 1

Djaouad
Djaouad

Reputation: 22784

You already have a while True: loop, you don't need the inner for loop to search for your number, just keep incrementing n in the while loop instead of adding a new counter, when the number you're looking for is found, the infinite while True: loop will stop (using break), and so your print statement will be executed:

n = 1001  #  start at 1001

while True:  #  start infinite loop
    if n % 33 == 0 and n % 273 == 0:  #  if `n` found
        break  #  exit the loop
    n += 1  #  else, increment `n` and repeat

print(f"The value of n is {n}")  #  done, print the result

Output:

The value of n is 3003

Upvotes: 4

rje
rje

Reputation: 6438

A for loop will not help you here, because you don't know when to end the loop. You usually use for loops when the range of things you want to loop over is already known.

Instead, do the following:

before starting your while: True loop: set i to 0,

then increase i with 1 every time to the loop

also, don't forget to stop the loop when i>1000!

Upvotes: 1

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