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The Least Common Multiple is generally seen in not only arithmetic but also the number theory. This Least Common Multiple is also known as the lowest common multiple or the smallest common multiple. And this is in turn the least common multiple of the 2 integers let us say, a & b. Furthermore, these integers are denoted in the following manner – LCM (a, b) which in turn happens to be the smallest positive integer that is divisible by ‘a’ as well as ‘b’.

## LCM Calculator

One has to remember the fact that the division of the integers especially by zero is not defined. Hence, when both a & b happen to be different from zero does the LCM or the least common multiple take place. In other words this LCM can also be said to be the lowest common denominator which is to be determined right before the fractions are either added or compared or for that matter subtracted.

And when the talk is about the LCM of 2 or (better) more than 2 integers then it is stated to be one of the smallest positive integer which is certainly divisible by both of them. The best example for this one can be that number 10 which is a multiple of 5 & the reason for this one would be that: . Hence, 10 is not only divisible by 2 but also 5. Therefore, number 10 is stated to be the smallest positive integer which is divisible by 5 as well as 2 apart from being the least common multiple of 5 & 2.

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Another example for this LCM can be the following fraction, let us have a look at it –

\(e.g.\frac{2}{21}+\frac{1}{6}=\frac{4}{42}+\frac{7}{42}=\frac{11}{42}\)

In the above equation, the denominator, 42 had been chosen as it is not only the least common multiple / LCM of 21 but also of number 6.

## Reduction with the help of GCD

GCD is also known as the greatest common divisor & or the greatest common factor & in order to compute this GCD, the following formula is put in to use –

\(lcm(a,b)=\frac{\left \| \quad a\times \quad b \quad \right \|}{gcd(a,b)}\)

\(e.g.\quad lcm=(21\times 6)=\frac{21\quad \times \quad 6}{gcd(\quad a\quad ,\quad b\quad )}=\frac{21 \times 6}{gcd( \quad3 \times \quad 6\quad )}=\frac{21 \times 6}{3}=\frac{126}{3}=42\)

**Check least common multiple with the help of the prime factorization**

\(e.g. \quad lcm(8,9,21)=\quad 2^{3}\quad.\quad3^{2}\quad .\quad 7^{1}\quad =8.\quad9.\quad 7=504\)

## How to use the least common multiple calculator?

To make use of the least common multiple calculator, you would be required to enter the numbers which are available in the box provided. But one has to remember the simple fact that the numbers are to be separated by commas similar to the way they have been mentioned above. Once the numbers are entered, click on the calculate tab to get to know the LCM or the least common multiple of the values entered. Thus this way one would be able to get to know as to the LCM of various values in a very simple manner.

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