LCM (9,100; 45,500) = ? Calculate the least common multiple, LCM, by two methods: 1) Numbers' divisibility and 2) The prime factorization

lcm (9,100; 45,500) = ?

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:


45,500 ÷ 9,100 = 5 + 0


=> 45,500 = 9,100 × 5


=> 45,500 is divisible by 9,100.


=> 45,500 is a multiple of 9,100.


The smallest multiple of 45,500 is the number itself: 45,500.


The least common multiple:
lcm (9,100; 45,500) = 45,500


lcm (9,100; 45,500) = 45,500 = 22 × 53 × 7 × 13
45,500 is a multiple of 9,100

Method 2. The prime factorization:

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


9,100 = 22 × 52 × 7 × 13
9,100 is not a prime number but a composite one.


45,500 = 22 × 53 × 7 × 13
45,500 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 (9,100; 45,500) = 22 × 53 × 7 × 13



lcm (9,100; 45,500) = 22 × 53 × 7 × 13 = 45,500
45,500 contains all the prime factors of the number 9,100


The final answer:
scroll down...

The least common multiple
lcm (9,100; 45,500) = 45,500 = 22 × 53 × 7 × 13
45,500 is divisible by 9,100. 45,500 is a multiple of 9,100.
45,500 contains all the prime factors of the number 9,100

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 9,100 and 45,500 = ? Sep 29 08:52 UTC (GMT)
The LCM of 0 and 0 = ? Sep 29 08:52 UTC (GMT)
The LCM of 120,148,200 and 120,148,200 = ? Sep 29 08:52 UTC (GMT)
The LCM of 210 and 6 = ? Sep 29 08:52 UTC (GMT)
The LCM of 3,940 and 394 = ? Sep 29 08:52 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.


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