Question

What is the LCM of $4,5$ and $10$?

Answer 1

Hint: In mathematics, the full form of the LCM is least common multiple. The LCM of any two or more numbers is the value which is evenly divisible by them. It is also called the least common divisor (LCD). LCM is a method to find the smallest common multiple between any two or more numbers. A common multiple is a number which is a multiple of two or more numbers.

Complete step by step solution:
The given numbers are $4,5$ and $10$. Now to find the LCM of the given number, we have to find our first common multiple of $4,5$ and $10$, it means we have to find the first number that can be divisible by $4,5$ and $10$ with no remainder.
Now write the multiples of $4,5$ and $10$. To get the LCM of these three numbers we have found out the common least multiple.
So , the multiples are:
The multiples of $4$: $4,8,12,16,20,24.....$
The multiples of $5$: $5,10,15,20,25,30,...$
The multiples of $10$: $10,20,30,40,...$
Now by comparing all the multiples of $4,5$ and $10$.we can see by above multiples only $20$ is the common and the least multiple of all the given numbers.

Hence the LCM of the $4,5$ and $10$ is $20$.

Note: LCM is also used to add or subtract any two fractions when the denominators of the fractions are different. While performing any arithmetic operations such as addition, subtraction with fractions, LCM is used to make the denominators common. This process makes the simplification process easier.