CLASS-6
FINDING LCM BY REPEATED DIVISION METHOD

FINDING LCM BY REPEATED DIVISION METHOD -

Example.1) Find the LCM of 18 and 24

  1. Start by finding the Greatest Common Divisor (GCD) of the two numbers. This can be done using various methods, such as prime factorization or the Euclidean algorithm.

      Prime factorization of 18: 18 = 2^1 * 3^2

      Prime factorization of 24: 24 = 2^3 * 3^1

      The common factors are 2^1 and 3^1.

       GCD = 2^1 * 3^1 = 2 * 3 = 6


    2. Now use the formula for finding the LCM using GCD: 

       LCM = (Number 1 * Number 2) / GCD 

       LCM = (18 * 24) / 6

       LCM = 432 / 6

           LCM = 72

So, the LCM of 18 and 24 is 72.    (Ans.)

In the division method, you first find the GCD of the numbers, and then you can find the LCM using the formula LCM = (Number 1 * Number 2) / GCD. This method provides a direct way to calculate the LCM without explicitly listing multiples or performing prime factorization.


Example.2) Find the LCM of 18 and 24 using the division method

  1. Start by listing the numbers 18 and 24.

    2. Find the greater number between the two (24 in this case) and divide it by the smaller number (18).

       24 ÷ 18 = 1 with a remainder of 6

    3. Now, take the divisor (18) and the remainder (6) and divide the previous divisor (18) by the remainder (6).

       18 ÷ 6 = 3 with no remainder

    4. Repeat the division process using the last divisor (6) and the new remainder (0).

       6 ÷ 0 = Undefined (since you cannot divide by 0)

    5. At this point, we have reached a remainder of 0. The last non-zero remainder obtained was 6.

    6. Now, write down the divisors used in the process: 18, 6, and 3.

        Divisors: 18, 6, 3

    7. The LCM is the product of the divisors. Multiply them together to get the LCM.

        LCM = 18 × 6 × 3 = 324

So, the LCM of 18 and 24 is 324.         (Ans.)

The division method involves repeatedly dividing the larger number by the smaller number and then using the divisors in the process to calculate the LCM. This method is straightforward and can be used to find the LCM of any pair of numbers.


Example.3) Find LCM of 24 and 36 by repeated division method.

Ans.)

lcm

So, LCM of 24 & 36 is 72.       (Ans.)