Question

Find the LCM by the method of division.

$9,15,16,35,36$

Answer 1

Find the required LCM

To find the LCM using Division Method, we induce the following steps:

Step $1$: Arrange all the numbers in a single row separated by commas.

Step $2$: Divide the arranged numbers by the prime numbers $2,3,5,7,11,...$.Start the division with the least prime that divides at least two of the given numbers exactly and so on.

Step $3$: Write down the quotients so obtained under their respective dividends.

Step $4$: Repeat Step $2$, until we get a row of numbers which are prime to each other.

Step $5$: Find the product of all the divisors and the numbers in the last row to get the LCM.

Here to find LCM of $9,15,16,35,36$ we use the above steps as:

Step $1$: Arrange $9,15,16,35,36$ in single row separated by commas.

Step $2$: Dividing by $2$, as it divides $16,36$. Carrying $9,15,35$ to the next row as they are not divisible by $2$.

Step $3$: Dividing by $2$, as it divides $8,18$. Carrying $9,15,35$ to the next row as they are not divisible by $2$.

Step $4$: Dividing by $3$, as it divides $9,15,9$. Carrying $4,35$ to the next row as they are not divisible by $3$.

Step $5$: Dividing by $3$ as it divides $3$ and $3$. Carrying $5,4,35$ to the next row as they are not divisible by $3$

Step $6$: Dividing by $5$ as it divides $5,35$. Carrying $4$ to the next row as it is not divisible by $5$

Since, no two numbers in the last row have a common prime divisor. Therefore, we stop here with the prime factorisation.

Step $7$: The required LCM can be obtained by taking the product of all the prime divisors (in the left vertical column) and the numbers in the last row.

Hence LCM $=2\times 2\times 3\times 3\times 5\times 4\times 7=5040$.

Therefore LCM of $9,15,16,35,36$ is $5040$.