Question

3. Find the LCM by common division method.
a) 21, 63, 105​

Answer 1

Answer:

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}3

1

, 7^{1}7

1

And

Uncommon prime factor = 5

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

1

, 3^{1}3

1

So,

Least Common Multiple = 3^{1}3

1

× 7^{1}7

1

× 5^{1}5

1

× 3^{1}3

1

= 315

Hence, The LCM using division method is 315 . Answer