Question

find the LCM of 105,315,693,1287 by division method​

Answer 1

Answer:

the LCM of ,105,315,693,1287 is 495495.

Answer 2

LCM of 105,315,693,1287 =   495495

Explanation:

Given:

LCM 105, 315, 693, 1287

To find: LCM

STEP 1: Find the prime factorization of 105

105 ÷ 5 = 21

 21 ÷ 3 = 7

   7 ÷ 7 = 1

Prime factorization of 105 is 5,3 and 7

STEP 2: Find the prime factorization of 315

315 ÷ 5 = 63

 63 ÷ 7 = 9

   9 ÷ 3 = 3

   3 ÷ 3 = 1

Prime factorization of 315 is 5,3,3 and 7

STEP 3: Find the prime factorization of 693

693 ÷ 3 = 231

 231 ÷ 3 = 77

   77 ÷ 11 = 7

     7 ÷ 7 = 1

Prime factorization of 693  is 3,3,11 and 7

STEP 4: Find the prime factorization of 1287

  1287 ÷ 3  = 429

   429 ÷ 3  = 143

   143  ÷ 143  = 1

 

Prime factorization of 1287 is 3,3 and 143

STEP 5: Find LCM of the Factors

Prime factorization of 105 =  5 × 3 × 7

Prime factorization of 315 =  5 × 3 × 3 × 7

Prime factorization of 693 =  3 × 3 × 11 × 7

Prime factorization of 1287 =  3 × 3 × 143

Taking common values,

LCM of 105,315,693,1287 =   5 × 3 × 3 × 7 × 11 × 143

LCM of 105,315,693,1287 =   495495