Question

L.C.M. of 15, 75, 225 is
A.45
B.15
C.225
D.None of these

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 15, 75, 225.
First write the multiple of all the three numbers,
Multiples of 15: 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240
Multiples of 75: 75 150 225 300 375 450
Multiples of 225: 225 450 675 900 1125
By the above observation it is clear that the 225 is the common multiple and it is also least common multiple. This method is known as the listing method.
The Lowest common multiple for 15, 75 and 225 is 225.
So, the correct answer is “Option C”.

Additional Information:
i.LCM stands for lowest common multiple. It is also known as the lowest common divisor.
ii.LCM can be found out by using the greatest divisor method, using prime factorization or by continuous division method.

Note: This question, can be solved by continuous division method as follows,
$
  5\left| \!{\underline {\,
  {15\,\,\,75\,\,\,225} \,}} \right. \\
  3\left| \!{\underline {\,
  {3\,\,\,\,\,\,\,15\,\,\,\,45} \,}} \right. \\
  3\left| \!{\underline {\,
  {1\,\,\,\,\,\,3\,\,\,\,\,\,15} \,}} \right. \\
  5\left| \!{\underline {\,
  {1\,\,\,\,\,\,\,\,1\,\,\,\,\,\,5} \,}} \right. \\
  \,\,\,\,1\,\,\,\,\,\,\,\,1\,\,\,\,\,\,1 \\
 $
Now, multiply the divisors to get the L.C.M.
So, L.C.M. of 15, 75 and 225 will be equal to $5 \times 3 \times 3 \times 5 \times 1 = 225$.
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.