Question

What is the Least Common Multiple (LCM) of 2 and 6?

Answer 1

Hint: To find the Least Common Multiple of 2 and 6, we have to list the multiples of 2 and 6. Then, we have to collect the first few common multiples. Then, the smallest one among these will be the LCM of 2 and 6.

Complete step by step solution:
We have to find the Least Common Multiple of 2 and 6. For this, we have listed the multiples of 2 and 6.
Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 28, 32, …
Multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66,….
We have to look for common multiples in 2 and 6. We can see that 6, 12, 18, 24, … are the common multiples. Of these, we have to choose the smallest multiple. We can see that 6 is the smallest multiple.

Therefore, LCM of 2 and 6 is 6.

Note: We can find LCM(2,6) in alternate methods. One of these is the prime factorization. Here, we will write 2 and 6 as the product of prime numbers.
Prime factorization of 2 is $2={{2}^{1}}$ .
Prime factorization of 6 is $2\times 3={{2}^{1}}\cdot {{3}^{1}}$
The least common multiple will be the product of all prime factors with the highest degree. Therefore, LCM (2,6) is ${{2}^{1}}\times {{3}^{1}}=6$
The other method is the long division method. We have to write the two numbers to the right and the left section will be their prime factors. We will divide each of the numbers by the prime factors and write the remainder below.
\[\begin{align}
  & 2\left| \!{\underline {\,
  2,6 \,}} \right. \\
 & 3\left| \!{\underline {\,
  1,3 \,}} \right. \\
 & \text{ }1,1 \\
\end{align}\]
LCM of 2 and 6 will be the product of all the prime factors. Therefore, LCM (2,6) is $2\times 3=6$