Question

Find the LCM of the $5,10,15,20$

Answer 1

Hint: First, we will see what LCM is.
LCM is the least common multiple of the given two or more than two numbers, first, we need to find the prime factors of the given number (for each given number)
and then we need to identify the all factors with the highest number of occurrences and finally we perform multiplication of the obtained numbers to get the least common multiple of the given terms.
From the given that, the numbers are in multiplication with five or five table numbers.

Complete step by step answer:
Since we need to find the LCM of the given numbers, which are $5,10,15,20$
First, we need to find the prime factorization of each number, which is the numbers that can be expressed or separated into the multiplication of the prime numbers only.
Thus take the first number $5$, here the given number itself is a prime number (five is a prime number) so we don’t need any changes in the given number five.
Second, take the number $10$, this number can be separated into the prime factorization as $10 = 2 \times 5$where two and five are prime numbers. Also the multiplication of two and five we get ten.
Similarly, take the next term $15$, this number can be separated into the prime factorization as $15 = 3 \times 5$
Where three and five are prime numbers.
Finally, take $20$, this number can be separated into the prime factorization as $20 = 2 \times 2 \times 5$, where two times the number two and five are the prime numbers.
This process can be generalized into the LCM method as follows,
$
  5\left| \!{\underline {\,
  {5,10,15,20} \,}} \right. \\
  2\left| \!{\underline {\,
  {1,2,3,4} \,}} \right. \\
  2\left| \!{\underline {\,
  {1,1,3,2} \,}} \right. \\
  3\left| \!{\underline {\,
  {1,1,3,1} \,}} \right. \\
  1\left| \!{\underline {\,
  {1,1,1,1} \,}} \right. \\
 $
Hence the left side entries are the least common values, which are $5,2,2,3$ and thus multiplying these values we get, $5 \times 2 \times 2 \times 3 = 60$
Therefore, the least common multiple $5,10,15,20$ is $60$

Note: First, we need to write the horizontal line and separate them. Then divide using the common prime numbers which exactly divides at least two given numbers, we put the quotient directly under the next row, hence continuing this process until we get all the entries as one.
This is called the LCM process for two or more numbers.
There is another concept like this, which is called the GCD the greatest common divisors.
We first find the common divisions of the given numbers and try to find which number is the greater value, and then if $\gcd (a,b) = 1$ then it is known as relatively prime, where the common divisors are number one only
Example: $\gcd (2,3) = 1$