Question

LCM of numbers 1, 2, 3 is equal to their
A.Product
B.Division
C.Sum
D.Difference

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:
Given, numbers are 1, 2, 3, we need to find the LCM of these three numbers.
First write the first eight multiple of all these three numbers.
 $ 1:\,1,\,2,\,3,\,4,\,5,\,6,\,7,\,8 $
 $ 2:\,2,\,4,\,6,\,8,\,10,\,12,\,14,\,16 $
 $ 3:\,3,\,6,\,9,\,12,\,15,\,18,\,21,\,24 $
Here, it can be observed that the common multiples are 6, 12,18, 24,……., but 6 is the common multiple and which is least common multiple. This method is known as the listing method.
The Lowest common multiple for 1, 2 and 3 is 6.
The product of 1, 2 and 3 is 6.
So, the correct answer is “Option A”.

Note: This question, can be solved by continuous division method as follows,
\[
  1\left| \!{\underline {\,
  {1\,\,\,2\,\,\,3} \,}} \right. \\
  2\left| \!{\underline {\,
  {1\,\,1\,\,\,3} \,}} \right. \\
  3\left| \!{\underline {\,
  {1\,\,1\,\,\,1} \,}} \right. \\
  \,\,\,1\,\,\,1\,\,\,1 \\
 \]
Now, multiply the divisors to get the L.C.M.
So, L.C.M. of 1, 2 and 3 will be equal to $ 1 \times 2 \times 3 = 6 $ .
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.