Symmetric Property

The LCM of 14 and 21 is the smallest positive integer, a multiple of both numbers. By finding the LCM, we can simplify the arithmetic operations with fractions to equate the denominators.

There are various methods to find the LCM, Listing method, prime factorization method and division method are explained below;

To ascertain the LCM, list the multiples of the integers until a common multiple is found. 

Steps:

              1. Write down the multiples of each number:  

Multiples of 14 = 14,28,42,…

Multiples of 21= 21,42,63…

2. Ascertain the smallest multiple from the listed multiples

The least common multiple of the numbers is 42.

The prime factors of each number are written, and then the highest power of the prime factors is multiplied to get the LCM.

Steps: 

1. Find the prime factors of the numbers:

Prime factorization of 14  = 2×7

Prime factorization of 21= 3×7

2. Take the highest power of each prime factor and multiply the ascertained factors.

— LCM = 42

The Division Method involves simultaneously dividing the numbers by their prime factors and multiplying the divisors to get the LCM. 

Steps:

1. Write down the numbers in a row;

2. Divide the row of numbers by a prime number that is evenly divisible into at least one of the given numbers. Continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers not divisible by the previously chosen prime number.

3. The LCM of the numbers is the product of the prime numbers in the first column, i.e, 

2×7×3 = 42