Question

What is the LCM of 4 and 16?

Answer 1

Hint: Here in this question we have been asked to find the LCM of 4 and 16. For answering this question we will first write the common multiples of 4 and 16 and then list out the common multiples and consider the least common multiple.

Complete step-by-step solution:
Now considering from the question we have been asked to find the LCM of 4 and 16.
From the basic concepts we know that LCM is the short form for Least common multiple.
The multiples of 4 can be listed as $4,8,12,16,20,24,.......$ .
Similarly the multiples of 16 can be listed as $16,32,48,64,............$.
If we observe the list of the multiples of 4 and 16 we can say that all multiples of 16 are multiples of 4 including 16 also since 16 is itself multiple of 4.
Hence we can conclude that the least common multiple of 4 and 16 will be 16.

Note: Generally many of us get confused between HCF and LCM. HCF stands for Highest Common Factor. We can also find the LCM by using a prime factorization method, that is we need to divide both the given numbers using prime numbers only as shown below.
$\begin{align}
  & 2\left| \!{\underline {\,
  4,16 \,}} \right. \\
 & 2\left| \!{\underline {\,
  2,8 \,}} \right. \\
 & 2\left| \!{\underline {\,
  1,4 \,}} \right. \\
 & 2\left| \!{\underline {\,
  1,2 \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
  1,1 \,}} \right. \\
\end{align}$
Hence we can say that the LCM of 4 and 16 is $2\times 2\times 2\times 2=16$ . We can say that the LCM of two numbers in which one is the multiple of other and greater than the other that like in this case then the number it is the least common multiple.