A method of dividing the numbers commonly by a number to find the least common multiple (LCM) of them is called the common division method.
The common division method is a simple method to find the lowest common multiple of the given numbers. In this method, we divide the given numbers commonly by a suitable number. There are four steps involved in this method.
Firstly, draw a perpendicularly intersected lines.
$\,\,\,$ | $\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$ |
$\,$ |
Write the given numbers $4,$ $8,$ $12,$ $16,$ $24$ and $36$ at right side of the vertical line but above the horizontal line.
$\,\,\,$ | $4, 8, 12, 16, 24, 36$ |
$\,$ |
All the given numbers are divisible by $2$. So, write it at left side of the vertical line and above the horizontal line.
$2$ | $4, 8, 12, 16, 24, 36$ |
$\,$ |
Every number is commonly divisible by $2$ and write each quotient at the corresponding position under the horizontal line.
$2$ | $4, 8, 12, 16, 24, 36$ |
$2, 4, \,\,\, 6, \,\,\, 8, 12, 18$ |
The numbers $2, 4, 6, 8, 12$ and $18$ can also be divisible by $2$. So, draw a horizontal line again and extend the vertical line to split it.
$2$ | $4, 8, 12, 16, 24, 36$ |
$2, 4, \,\,\, 6, \,\,\, 8, 12, 18$ | |
$\,$ | $\,$ |
Now, write $2$ at left side of the vertical line and over the horizontal line, and then write the quotients below the horizontal line.
$2$ | $4, 8, 12, 16, 24, 36$ |
$2$ | $2, 4, \,\,\, 6, \,\,\, 8, 12, 18$ |
$\,$ | $1, 2, \,\,\, 3, \,\,\, 4, \,\,\, 6, \,\,\, 9$ |
In the numbers $1, 2, 3, 4, 6$ and $9,$ the numbers $2, 4$ and $6$ are divisible by $2$ and the remaining numbers are indivisible. So, repeat the same procedure. Write the quotients in the respective positions but write the undivided numbers as they are, below the horizontal line.
$2$ | $4, 8, 12, 16, 24, 36$ |
$2$ | $2, 4, \,\,\, 6, \,\,\, 8, 12, 18$ |
$2$ | $1, 2, \,\,\, 3, \,\,\, 4, \,\,\, 6, \,\,\, 9$ |
$\,$ | $1, 1, \,\,\, 3, \,\,\, 2, \,\,\, 3, \,\,\, 9$ |
The numbers $3, 3$ and $9$ are divisible by $3$ and the remaining numbers are indivisible. So, repeat the process one more time.
$2$ | $4, 8, 12, 16, 24, 36$ |
$2$ | $2, 4, \,\,\, 6, \,\,\, 8, 12, 18$ |
$2$ | $1, 2, \,\,\, 3, \,\,\, 4, \,\,\, 6, \,\,\, 9$ |
$3$ | $1, 1, \,\,\, 3, \,\,\, 2, \,\,\, 3, \,\,\, 9$ |
$\,$ | $1, 1, \,\,\, 1, \,\,\, 2, \,\,\, 1, \,\,\, 3$ |
There are no at least two divisible numbers in the numbers $1, 1, 1, 2, 1$ and $3$. So, we can stop the procedure.
In this example, the divisors are $2, 2, 2$ and $3$ and the undivided numbers $1, 1, 1, 2, 1$ and $3$. The product of them is called least common multiple.
$L.C.M$ $\,=\,$ $2$ $\times$ $2$ $\times$ $2$ $\times$ $3$ $\times$ $1$ $\times$ $1$ $\times$ $1$ $\times$ $2$ $\times$ $1$ $\times$ $3$
$\therefore \,\,\,\,\,\,$ $L.C.M \,=\, 144$
In this way, the LCM of the given numbers is calculated in the common division method.
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