Question

Find the LCM by the method of division.

$8,24,48,80,102$

Answer 1

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 $8,24,48,80,102$ we use the above steps as:

Step $1$: Arrange $8,24,48,80,102$ in single row separated by commas.

Step $2$: Dividing by $2$, as it divides all the numbers.

Step $3$: Dividing by $2$, as it divides $4,12,24,40$. Carrying $51$ to the next row as it is not divisible by $2$.

Step $4$: Dividing by $2$, as it divides $2,6,12,20$. Carrying $51$ to the next row as it is not divisible by $2$.

Step $5$: Dividing by $3$ as it divides $3,6$ and $51$. Carrying $10$ to the next row as it is not divisible by $3.$

Step $6$: Dividing by $2$ as it divides $2,10$. Carrying $17$ to the next row as it is not divisible by $2.$

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 $=2\times 2\times 2\times 3\times 2\times 5\times 17=4080$.

Therefore LCM of $8,24,48,80,102$ is $4080$.