LCM (3; 9) = ? Calculate the least common multiple, LCM, by two methods: 1) Numbers' divisibility and 2) The prime factorization

lcm (3; 9) = ?

Method 1. The divisibility of numbers:

A number 'a' is divisible by a number 'b' if there is no remainder when 'a' is divided by 'b'.


Divide the larger number by the smaller one.


When we divide our numbers, there is no remainder:


9 ÷ 3 = 3 + 0


=> 9 = 3 × 3


=> 9 is divisible by 3.


=> 9 is a multiple of 3.


The smallest multiple of 9 is the number itself: 9.


The least common multiple:
lcm (3; 9) = 9


lcm (3; 9) = 9 = 32
9 is a multiple of 3

Method 2. The prime factorization:

The prime factorization of a number: finding the prime numbers that multiply together to make that number.


3 is a prime number, it cannot be broken down into other prime factors.


9 = 32
9 is not a prime number but a composite one.


* The natural numbers that are only divisible by 1 and themselves are called prime numbers. A prime number has exactly two factors: 1 and itself.
* A composite number is a natural number that has at least one other factor than 1 and itself.



Calculate the least common multiple, lcm:

Multiply all the prime factors of the two numbers, taken by the largest exponents (largest powers).


lcm (3; 9) = 32



lcm (3; 9) = 32 = 9
9 contains all the prime factors of the number 3


The final answer:
scroll down...

The least common multiple
lcm (3; 9) = 9 = 32
9 is divisible by 3. 9 is a multiple of 3.
9 contains all the prime factors of the number 3

Why is it useful to calculate the least common multiple?

When adding, subtracting or sorting fractions with different denominators, in order to work with those fractions we must first make the denominators the same. An easy way is to calculate the least common multiple of all the denominators of the fractions (the least common denominator).


By definition, the least common multiple of two numbers is the smallest natural number that is: (1) greater than 0 and (2) a multiple of both numbers.


The least common multiple, LCM: the latest 5 calculated values

The LCM of 3 and 9 = ? Nov 28 11:32 UTC (GMT)
The LCM of 6,624 and 5 = ? Nov 28 11:32 UTC (GMT)
The LCM of 120 and 300 = ? Nov 28 11:32 UTC (GMT)
The LCM of 729 and 3 = ? Nov 28 11:32 UTC (GMT)
The LCM of 243 and 125 = ? Nov 28 11:32 UTC (GMT)
The least common multiple, LCM: the list of all the operations

Calculator: calculate the least common multiple, lcm

Calculate the least common multiple of the numbers, LCM:

Method 1: Run the prime factorization of the numbers - then multiply all the prime factors of the numbers, taken by the largest exponents.

Method 2: The Euclidean algorithm:
lcm (a; b) = (a × b) / gcf (a; b)

Method 3: The divisibility of the numbers.

The least common multiple (lcm). What it is and how to calculate it.

Some articles on the prime numbers

What is a prime number? Definition, examples

What is a composite number? Definition, examples

The prime numbers up to 1,000

The prime numbers up to 10,000

The Sieve of Eratosthenes

The Euclidean Algorithm

Completely reduce (simplify) fractions to the lowest terms: Steps and Examples