Question

What would be the L.C.M. of 12, 18, 24?
A.72
B.144
C.36
D.120

Answer 1

Hint: To find the LCM of the given number we need to find the multiples of each individual number and then we need to select the common multiple among all the three and then whichever number is the least is the lowest common multiple.

Complete step-by-step answer:
LCM stands for lowest common multiple. It is also known as lowest common divisor.
LCM can be found out by using the greatest divisor method, using prime factorization or by continuous division method.
Given, numbers are 12, 18, 24.
First write the multiple of all the three numbers,
$\Rightarrow$ Multiples of 12: 12 24 36 48 60 72
$\Rightarrow$ Multiples of 18: 18 36 54 72 90 108
$\Rightarrow$ Multiples of 24: 24 48 72 96 120 144
By the above observation it is clear that the 72 is the common multiple and it is also least common multiple. This method is known as the listing method.
The Lowest common multiple for 12, 18 and 24 is 72.

So, the correct answer is “Option A”.

Note: This question, can be solved by continuous division method as follows,
$
  2\left| \!{\underline {\,
  {12\,\,\,18\,\,\,24} \,}} \right. \\
  3\left| \!{\underline {\,
  {6\,\,\,\,\,\,\,9\,\,\,\,12} \,}} \right. \\
  2\left| \!{\underline {\,
  {2\,\,\,\,\,\,3\,\,\,\,\,\,4} \,}} \right. \\
  3\left| \!{\underline {\,
  {1\,\,\,\,\,\,\,\,3\,\,\,\,\,\,2} \,}} \right. \\
  2\left| \!{\underline {\,
  {1\,\,\,\,\,\,\,\,1\,\,\,\,\,\,2} \,}} \right. \\
  \,\,\,\,1\,\,\,\,\,\,\,\,1\,\,\,\,\,\,1 \\
 $
Now, multiply the divisors to get the L.C.M.
$\Rightarrow$ So, L.C.M. of 12, 18 and 24 will be equal to $2 \times 3 \times 2 \times 3 \times 2 \times 1 = 72$.
There is one more way to solve this problem by factor tree method, in this method we have to find all the factors of the given number, then by making the pairs we can find the L.C.M.