Question

What is the least common multiple (LCM) of 4 and 7?

Answer 1

Hint: To find the LCM of 4 and 7, we have to list a few multiples of 4 and 7. We will then check the common multiples of 4 and 7. We will then take the lowest multiple which will be the LCM of 4 and 7.

Complete step by step solution:
We have to find the LCM of 4 and 7. LCM means least common multiple. So we have to list a few multiples of 4 and 7.
Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, …
Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, …
We can see that the common multiples of 4 and 7 are 28, 56, and so on. We need the least common multiple which means the lowest multiple. Hence, the LCM of 4 and 7 is 28.

Note: Students should not be confused with LCM and HCF. HCF is the highest common factor. We can also find the LCM using a common division method.
We will first divide the given numbers by using only prime numbers.
$\begin{align}
  & 2\left| \!{\underline {\,
  4,7 \,}} \right. \\
 & 2\left| \!{\underline {\,
  2,7 \,}} \right. \\
 & 7\left| \!{\underline {\,
  1,7 \,}} \right. \\
 & \text{ }1,1 \\
\end{align}$
We have to multiply the factors. Therefore LCM of 4 and 7 is $2\times 2\times 7=28$ .
We can also find LCM using prime factorization. Here, we have to write each number as a product of all the prime factors of the given set.
Prime factor of 4 is $2\times 2={{2}^{2}}$ .
Prime factor of 7 is 7.
Now we have to multiply all the prime factors with the highest degree.
Hence, LCM of 4 and 7 is ${{2}^{2}}\times 7=2\times 2\times 7=28$ .