Question

How do you find the LCM of $24/36$.

Answer 1

Hint:
In order to find the LCM the student should know what LCM means. LCM is the acronym for Least Common Multiple. It is a smallest number which is a multiple of all the given numbers for which LCM has to be found out. Terms Students need to break down the given number in terms of its prime factors. Then the multiples appearing maximum number of times between the two numbers should multiply to find the LCM. Students can directly find out the LCM if the numbers are small or can use the formula $LCM(a,b) = \dfrac{{|a \times b|}}{{\gcd (a,b)}}$, where $a\& b$ numbers and GCD are is the greatest common divisor of the numbers.

Complete step by step solution:
First Method
First step is to break down the number in terms of its prime factors. So the number in terms of its prime factors is
$
  24 = 2 \times 2 \times 2 \times 3 \\
  36 = 2 \times 2 \times 3 \times 3 \\
$
Now multiplying the multiples occurring maximum number of times , i.e. LCM would be $2 \times 2 \times 2 \times 3 \times 3$
Thus the LCM of $24/36$is $72$

Second Method
In this method we use the formula $LCM(a,b) = \dfrac{{|a \times b|}}{{\gcd (a,b)}}$.
We can substitute $24\& 36$as $a\& b$ in the above formula
$LCM(24,36) = \dfrac{{|24 \times 36|}}{{\gcd (24,36)}}$
We can say that GCD of $24\& 36$ is $12$
Substituting the value in the formula we get the LCM
$LCM(24,36) = \dfrac{{24 \times 36}}{{12}}$
=$72$

Note:
Though we have used formulas in this particular sum, it is advisable to use the first method to solve all LCM related numerical. It’s because this method is easy to understand and solve. Only thing a student should know in the first method is to simplify the given numerical in terms of its prime factors. Students should try and restrict themselves to learn a minimum number of formulas to solve such a type of a sum.