Python calculation error

Question

I am trying to implement an LCM finding algorithm. It needs to find LCM for very large numbers.

LCM is found using the formula,

LCM(A, B) = (A * B) / GCD(A, B)

where A and B are two inputs.

Input: 226553150 1023473145
So, LCM = (226553150 * 1023473145) / 5
It should be, 46374212988031350.

But python is finding this as 46374212988031352, which is obviously an error. How to solve this problem ? python screenshot

You can read more about the limits of floating points here: https://docs.python.org/2/tutorial/floatingpoint.html — Keiwan, May 21 '16 at 15:54
Looks like this is a Coursera course, I see there's a [C question on the same subject](http://stackoverflow.com/questions/36540103/lowest-common-multiple-with-doubles-in-c). — Martijn Pieters, May 21 '16 at 16:12

Martijn Pieters · Answer 1 · 2018-07-20T16:01:59.857

You are using floating point math, because you used the / true division operator. Floating point can only approximate large numbers, and the difference you see is a result of that.

Use // floor division instead:

>>> (226553150 * 1023473145) // 5
46374212988031350

Floor division on integers never requires conversion to float, avoiding the precision issues.

Alternatively, use the decimal module for higher-precision math with real numbers:

>>> from decimal import Decimal
>>> Decimal('226553150') * Decimal('1023473145') / Decimal('5')
Decimal('46374212988031350')

This is slower than using float.

Python calculation error

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