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**Hint:**To know the specific difference between lemma and algorithm we first have to know what they are. Lemma is a proven statement that is used to prove another statement whereas algorithms are the series of well defined steps used to solve a problem. Although they both appear to be the same but are different.

**Complete step-by-step solution:**

We will start by defining lemma and algorithm.

So lemma is a proven proposition that is used in proving bigger results. It is kind of a theorem but the one which helps us to find the bigger one that is the reason it is known as “helping theorem”. For example- Euclid’s Division Lemma which state that if we have two positive integers $a,b$ then there will be two whole number $p,q$ which satisfy the below equation:

$a=bp+q$ Where $0\le q< b$

Next Algorithm is a description of steps that can be used to solve a mathematical computation; they are the efficient way to do math. They are basically a shortcut to solve a much complex problem. For example- Pythagoras Theorem which states that sum of square of base and height of the right –angle triangle is equal to square of the Hypotenuse which is given as:

${{H}^{2}}={{B}^{2}}+{{P}^{2}}$

Where,

$H=$ Hypotenuse

$P=$Perpendicular

$B=$ Base

**So the difference between both of them is that although they have the same set of patterns they exhibit in a different sense.**

**Note:**Some more information above lemma is that it derives its importance from the theorem it aims to prove. Lemma is denoted as a minor result whose sole purpose is to help in proving a theorem. Algorithms is one that is the easy way to do any problem like if we want to find 9785 times 679 times we can either do it in 679 step where we add the number that much time or we can simply use the algorithm and multiply both the numbers which is less time consuming and less complicated.

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