Least Common Multiple (L.C.M)

The least number which is exactly divisible by each one of the given numbers.

Least Commmon Multiple(L.C.M) can be calculated by any of the following methods:

Factorization Method:
Express each one of the numbers as product of prime factors.
The product of highest powers of all prime factors gives LCM.

Example:
Least Common Multiple of 36, 90, 72.

Step1: Express the numbers as product of prime factors.
       36 = 2² × 3²
       90 = 2 × 5 × 3²
       72 = 2³ × 3²

Step2: Take the prime numbers with highest power for all prime numbers.
2, 3,5 are the prime number identified.

       The highest power of 2 in the set is - 2³
       The highest power of 3 in the set is - 3²
       The highest power of 5 in the set is - 5

Step3: Product of the numbers taken.
       3² × 5 × 2³ = 9 × 5 × 8 = 360

       So 360 is the LCM of the numbers.

Common Division Method:

Place the numbers in any order in a row. Divide the numbers(dividends) by a number(divisor) which exactly divides atleast two of them. Write the quotients of the divided numbers below them in the next row along with the undivided numbers.

Repeat the above steps untill two numbers are left out which are not divisible by a same number except 1.

The product of the divisors and the undivided numbers is the required L.C.M.

Example:

Taking the previous example we approach as follows:

     2 | 36      90      72

     2 | 18      45      36

     9 |  9       45      18

        |  1        5        2

Therefore, the L.C.M of the given numbers is 2 × 2 × 9 × 5 × 2 = 360.

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Posted in: Common Division Method,Factorization Method,L.C.M,Numerical Operations