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How do you find the LCM of $2$and $13$?

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Last updated date: 29th Feb 2024
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IVSAT 2024
Answer
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Hint: In this question we have to find the LCM which is the abbreviation of the term lowest common multiple which tells us the lowest number which is present in the mathematical table of both the numbers. We will find the lowest common multiple by writing the multiples of both the terms till we find the first common multiple for both the numbers.

Complete step-by-step answer:
We have the numbers $2$ and $13$.
On writing the multiples of $2$, we get:
$2,4,6,8,10,12,14,16,18,20,22,24,26,28......$
Now on writing the multiples of $13$, we get:
$13,26,39,52,65.......$
Now from the above multiples of $2$ and $13$, we can see that the first term which is a multiple for both the numbers is $26$, therefore the lowest common multiple is $26$.

Note: The lowest common multiple can also be found using the prime method. In this method both the terms should be written as a product of prime numbers. Since the numbers $2$ and $13$, both are prime numbers they cannot be expressed as a product of prime numbers therefore, the lowest common multiple is the multiplication of the term $2$ and $13$, which is $26$.
There also exists the HCF of a number which is the abbreviation for highest common factor of a number which tells the greatest number by which two numbers can be divided such that there is no remainder. It can be found out by multiplying the common prime factors which have the lowest degree.