Question

Find LCM of $12,18$ and $24$

Answer 1

Hint: We have been given with three numbers and we have to find their LCM. LCM is the lowest common multiple of the number. Now, firstly, we have to find the prime factor of each number, then we write the number as the product of their prime factors. Then, we write the factors in power forms. As LCM is the lowest common multiple, we take each factor with their highest component and write them in product form. The product of these factors will be the LCM of the numbers.

Complete step-by-step answer:
The given numbers are $12,18$ and $24$.
We have to find their LCM.
Firstly, do the prime factorization of the numbers.
Prime factors of $12 = 2 \times 2 \times 3 \times 1 = {2^2} \times 3 \times 1$
$ \Rightarrow 12 = {2^2} \times 3 \times 1$
Prime factors of $18 = 2 \times 3 \times 3 \times 1$
$ \Rightarrow 18 = 2 \times {3^3} \times 1$
Prime factors of $24 = 2 \times 2 \times 2 \times 3 \times 1$
$ \Rightarrow 24 = {2^3} \times 1$
So, we have
$12 = {2^2} \times 3 \times 1$
$18 = 2 \times {3^2} \times 1$
$24 = {2^3} \times 3 \times 1$
LCM of $12,18$ and $24 = {2^3} \times {3^2} \times 1$
$ = 2 \times 2 \times 2 \times 3 \times 3$

Answer is $ = 72$

Note: The number which can be divided by itself and one only is called prime number. In number theory, integral factorization is the decomposition of composite numbers into the product of smaller integers if these smaller integers are restricted to prime numbers only. LCM of three numbers is the smallest common multiple or a positive integer which is divisible completely by both the numbers. We can use L.C.M to solve daily problems or use various algorithms such as racetracks, traffic lights, etc.