Finding the LCM of 3 and 6

6 is the LCM of 3 and 6.  

The smallest positive integer and a multiple of both numbers is the LCM.
 

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

 use the following steps to find the LCM

Step 1: Write down the multiples of each number

  — Multiples of 3 = 3,6,9,12,18 …

  — Multiples of 6 = 6, 12,18,24,…

Step 2:  Ascertain the smallest multiple from the listed multiples

— The smallest common multiple is 6.

Thus, LCM(3, 6) = 6.

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

Step1: Write the prime factors of the numbers:

  — Prime factorization of 

3 = 3

6 = 2×3

Step2: Pick the highest powers of each prime factor:

  — Highest power of 3 = 3

  — Highest power of 6 = 2

Step3: highest powers are to be multiplied to get the LCM:

        LCM(3, 6) = 3 × 2= 6

Step 1: Write the numbers in a row

Step 2: Divide by common prime factors and multiply the divisors: 

  — 3 × 2 = 6

Thus, LCM(3, 6) = 6.

 

• Multiple — It is a product of a number and any natural integer. So for 6, 6,12,18,..etc are the multiples. 

• Prime Factor — It is a prime number that one gets after factorization of any given number. Like for 6 - 2,3, and 6 are prime factors as they can be divided by 1 or the number itself.

• Prime Factorization — It is a process of dividing the number into prime factors.

• Co-prime numbers — These are the positive integers where both the numbers can be divided only by 1. 

• Fraction — It is expressed as part of a whole, in which the numerator is divided by the denominator, so for a fraction like 3/6– 3 is the numerator and 6 is the denominator. Proper fraction is where numerator is always lesser than denominator.