LCM of 3 and 7

The LCM of 3 and 7 is 21 which is the smallest positive integer, a multiple of both numbers. 
 

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

The LCM of 3 and 7 can be found using the following steps;

Step 1:Write down the multiples of each number:  

Multiples of 3 = 3,6,9,12,15,18,21,…

Multiples of 7 = 7,14,21,…

Step 2:find the smallest multiple from the listed multiples of 3 and 7. 

LCM(3,7) = 21

21 is divisible by 3 and 7 leaving no reminders. 
 

The numbers are prime factorized and their highest powers are multiplied.     

Step 1: Write the prime factors of the numbers:

Prime factorization of 3 = 3

Prime factorization of 7  = 7

Step 2:  Pick the highest power of each prime factor:

3,7

Step 3: Multiply the factors to get the LCM: 

LCM (3,13) = 3×7 = 21
 

Here we divide the numbers by their prime factors and multiplying the divisors to get the LCM.

Step 1: Write the numbers in a row;

Step 2:Divide the row of numbers with a number that is evenly divisible into at least one of the given numbers, and continue dividing the numbers until the last row of the results is ‘1’ and bring down the numbers has not been divisible previously.
   
Step 3: The LCM of the numbers is the product of the divisors

3×7= 21

LCM (3,7) = 21
 

• Multiple: A number and any integer multiplied. 

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

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

• Co-prime numbers: When the only positive integer that is a divisor of them both is 1, a number is co-prime.

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

• Fraction: A representation of a part of a whole.