Question

Find the LCM of $80,96,125,160$

Answer 1

To find LCM of $80,96,125,160$ we will use the method of division.

The following steps will help us to get through the solution:

Step $1$: Arrange $80,96,125,160$ in single row separated by commas.

Step $2$: Dividing by $2$, as it divides $80,96$ and $160$, while carrying $125$ to the next row as it is not divisible by $2$.

Step $3$: Dividing by $2$ as it divides $40,48$ and $80$, while carrying $125$ to the next row as it is not divisible by $2$.

Step $4$: Dividing by $2$ as it divides $20,24$ and $40$, while carrying $125$ to the next row as it is not divisible by $2$.

Step $5$: Dividing by $2$ as it divides $10,12$ and $20$, while carrying $125$ to the next row as it is not divisible by $2$.

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Step $6$: Dividing by $2$ as it divides $6,10$, while carrying $5$ and $125$ to the next row as they are not divisible by $2$

Step $7$: Dividing by $5$ as it divides $5$ and $25$, while carrying $3$ 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 $8$: 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 $=2\times 2\times 2\times 2\times 2\times 5\times 3\times 25=12000$.

Therefore LCM of $80,96,125,160$ is $12000$.