Question

Find the lcm of the division method , 21 ,63 ,105

Answer 1

Given :

The number are 21 , 63 , 105

To Find :

The LCM using division method

Solution :

Decompose all the numbers into prime factor

Applying Long Division Method

So,

Prime factor of 21 = 3 × 7

Prime factor of 63 = 3 × 3 × 7

Prime factor of 105 = 3 × 5 × 7

Now,

Common prime factor = 3 , 7

Highest power of common prime factor = $3^{1}$ , $7^{1}$

And

Uncommon prime factor = 5

Highest power of uncommon prime factor = $5^{1}$ , $3^{1}$

So,

Least Common Multiple  =   $3^{1}$  × $7^{1}$  ×  $5^{1}$  × $3^{1}$

                                         = 315

Hence, The LCM using division method is 315  . Answer