LCM of 6 and 7

The LCM of 6 and 7 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; 
 

The LCM of 6 and 7 can be found using the following steps:

Step 1: Write down the multiples of each number

Multiples of 6 = 6,12,…42,…

Multiples of 7 = 7,14,…42,…

Step 2: Ascertain the smallest common multiple from the listed multiples

  The smallest common multiple is 42

Thus, LCM(6, 7) = 42.
 

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

Step 1: Find the prime factors of the numbers:

Prime factorization of 6 = 2×3

 Prime factorization of 7 = 7

Step 2: Take the highest powers of each prime factor:

Highest power of prime factors= 2,3

Highest power of prime factor = 7

Step 3: Multiply the highest powers to get the LCM:

LCM(6, 7) =   2 ×3 × 7= 42

Thus, LCM(6, 7) = 42.

 

This method involves dividing both numbers by their common prime factors until no further division is possible, then multiplying the divisors to find the LCM.

Step 1: Write the numbers, divide by common prime factors and multiply the divisors.

Step 2:  A prime integer that is evenly divisible into at least one of the provided numbers should be used to divide the row of 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.

Step 3:   2× 3 × 7= 42

Thus, LCM(6, 7) = 42.



 

• Prime Factor: A natural number (other than 1) whose factors are only one and itself.

• Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. 

• Relatively Prime Numbers: Numbers that have no common factors other than 1.