Find the LCM of 105,135 and 150 by common division method.

Given :

The given numbers are 135, 105, 150.

To do :

We have to find the LCM of the given numbers.

Solution :

• First Write the given numbers in a horizontal line
  

                                   135, 105,  150

• Divide them by a suitable prime number, which exactly divides at least two of the given numbers. 
  

                                3 | 135, 105,  150

• We put the quotient directly under the numbers in the next row.  If the number is not divided exactly, we bring it down in the next row. We continue the process until there are no common divisors numbers are left in the last row

                               3 | 45,  35,  50

                               5 | 15,  35,  50

                               5 | 3,  7,  10

We multiply all the prime numbers by which we have divided and numbers left in the last row.  This will give LCM

$LCM= 3\times 3\times 5\times 1\times 7\times 10$

$=3150$

Therefore, LCM of 105, 135, 150 is 3150.

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Updated on: 10-Oct-2022

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