Question

What is the L.C.M of \[4\] and \[6\]?

Answer 1

Hint: This question is based on the Least Common Factor (L.C.M). The least number which is exactly divisible by each one of the given numbers is called their L.C.M. Here we will use the factorisation method of finding L.C.M. In this method, resolve each one of the given numbers into a product of prime factors. Then, L.C.M. is the product of the highest powers of all the factors.

Complete step-by-step answer:
Here in this question we have been asked to find the L.C.M of \[4\] and \[6\]. Now by using the factorization method of L.C.M. Let's find the L.C.M. First write the given numbers as the product of their prime factors. A number that is divisible only by itself and \[1\] is called prime number, example \[2{\text{,}}3{\text{,}}5{\text{,}}7{\text{,etc}}{\text{.}}\]
Let us write factors of \[4\] and \[6\] in terms of prime numbers.
\[4 = {2^2}\]
\[6 = {2^1} \times {3^1}\]
Here, we can see that the highest power of the prime factors \[2\] is \[2\] and \[3\] is \[1\]. Now multiply \[{2^2} \times {3^1}\] to get the L.C.M.
L.C.M. of \[4\] and \[6 = {2^2} \times {3^1}\]
\[ = 2 \times 2 \times 3\]
\[ = 12\].
Hence the L.C.M. of \[4\] and \[6\] is \[12\].
So, the correct answer is “12”.

Note: There is one more method to find L.C.M, called the Common Division (Short-cut) Method of finding L.C.M. In this method, arrange the given numbers in a row in any order. Divide by a number which divides exactly at least two of the given numbers and carry forward the numbers which are not divisible. Repeat the above process till no two of the numbers are divisible by the same number except \[1\]. The product of the divisions and the undivided number is the required L.C.M of the given numbers.
Let's solve the given question in this method.
\[
  2\left| \!{\underline {\,
  {4,6} \,}} \right. \\
  {\text{ 2,3}} \;
 \]
Here \[4\] and \[6\] is first divided by \[2\] and gets the result \[2,3\] which cannot be further divided because \[2\] and \[3\] are the prime numbers. Further division of prime numbers will result in the same number.
Now by multiplying the divisions and the undivided number we will get the L.C.M. \[ = 2 \times 2 \times 3 = 12\].