Question

Find the LCM of each of the following groups of number, using
(i). The prime factor method and
(ii). The common division method:
$14,21,98$

Answer 1

Hint: First, we are given three numbers $14,21,98$ and then we are asked to find the LCM of them in two ways.
We first need to know about the LCM, which is the least common multiple of the given numbers, we will find its common multiple and then convert it into the prime factor multiple and finally take the least among them.

Complete step-by-step solution:
Since from the given that we have to find the lowest common multiple of $14,21,98$
The numbers $14,21,98$ are not prime numbers because Prime numbers are the numbers that are divisible by themselves and $1$ only or also known as the numbers whose factors are the given number itself. Thus these numbers are composite numbers which is the composite number because the composite numbers which are divisible by themselves, $1$ and also with some other numbers (at least one number other than $1$ and itself). Also, according to the composite number definition, the composite number can be expressed as the product of the prime numbers.
Hence $14$ can be written as a prime factor of $14 = 2 \times 7$ and the number $21$ can be written as a prime factor of $21 = 3 \times 7$ and also the number $98$ can be written as a prime factor of $98 = 2 \times 7 \times 7$
Thus we have the LCM as $7 \times 7 \times 2 \times 3$ (factor method)
Now to find the LCM of the given three numbers we use the LCM (division) table which is
$
  7\left| \!{\underline {\,
  {14,21,98} \,}} \right. \\
  7\left| \!{\underline {\,
  {2,3,14} \,}} \right. \\
  2\left| \!{\underline {\,
  {2,3,2} \,}} \right. \\
  3\left| \!{\underline {\,
  {1,3,1} \,}} \right. \\
  1\left| \!{\underline {\,
  {1,1,1} \,}} \right. \\
 $
Thus, we get the LCM of $14,21,98$ as $7 \times 7 \times 2 \times 3$ and then by the multiplication operation we have $7 \times 7 \times 2 \times 3 = 294$
Hence the LCM of $14,21,98$ is $294$ (which is the common division method).

Note: The LCM stands for Least common multiple or lowest common multiple. The LCM of a number is the smallest number that is the product of two or more than two numbers. There is more than one method to find the LCM. The quickest way is using the prime factors of each number and then producing the least powers of the common prime factors.