Question

Find the LCM of $ 4,6 $ and $ 12 $

Answer 1

Hint: LCM (Least common Multiple) is expressed as the least or the smallest number with which the given numbers are exactly divisible without any remainder. It is also known as the least common divisor. Here first of all we will find the prime factors for all the given numbers and then will identify LCM.

Complete step-by-step answer:
Prime factorization is defined as the process of finding which prime numbers can be multiplied together to make the original number, where prime numbers are expressed as the numbers greater than $ 1 $ and which are not the product of any two smaller natural numbers. For Example: $ 2,{\text{ 3, 5, 7,}}...... $ where $ 2 $ is the prime number as it can have only $ 1 $ factor.
Here we will find the product of prime factors one by one for all the given numbers.
 $
  4 = 2 \times 2 \\
  6 = 2 \times 3 \\
  12 = 2 \times 2 \times 3 \;
$
LCMs are defined as the product of highest power of each factor involved in the numbers.
Therefore, the LCM of the given three numbers $ 4,6 $ and $ 12 $ is $ 2 \times 2 \times 3 = 12 $
So, the correct answer is “12”.

Note: To solve these types of sums, you should be very clear with the concept of HCF and LCM and the prime numbers. HCF is expressed as the highest or greatest common multiple whereas the LCM can be defined as the least common multiple or least common divisor in two or more given numbers. Also, remember that we get the prime factorization of any composite number in the form of multiples. Be good in multiples and remember at least till twenty.