Question

Find the LCM of the following numbers by prime factorization method.

Answer 1

Hint: The prime number is the number that is divisible by only 1 and itself. So the prime factorization method is that the factorization of any number that should consist of only prime numbers and no other numbers like even and odd should be involved in the factorization.

Complete step-by-step answer:
The given numbers are 48, 56 and 72 and we have to find the Least common factor using the prime factorization.
We know the prime factorization of 48, 56 and 72 is given as,
\[\begin{array}{l}
2\left| \!{\underline {\,
  {48,\,56,\,72} \,}} \right. \\
\,\,\left| \!{\underline {\,
  {24,28,36} \,}} \right.
\end{array}\]
Now, again we will take 2 as the factor, then,
\[\begin{array}{l}
2\left| \!{\underline {\,
  {12,14,18} \,}} \right. \\
\,\,\left| \!{\underline {\,
  {6,7,9} \,}} \right.
\end{array}\]
Now, the numbers 6 and 9 can be divisible by 3 and at the same time it is a prime number so taking 3 as the factor, we get the value as,
\[\left| \!{\underline {\,
  {2,7,3} \,}} \right. \]
Now, it can be observed that all the factors 2, 3, and 7 are primes, then the output will be,
 \[2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7\]
 Then after multiplying the factors, we will get,
 $ 1008 $
Therefore, 1008 is the LCM of the numbers 48, 56 and 72 using the prime factorization method.

Note: o, before factoring the given numbers, it should be noted that the primes are the only numbers that should be involved while factoring the given numbers. And the procedure should be step by step and it should be taken care that the factors should be least one while taking we should not go for big prime numbers.