LCM (26,584; 159,504) = ? Calculate the least common multiple, LCM, by two methods: 1) Numbers' divisibility and 2) The prime factorization

lcm (26,584; 159,504) = ?

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:


159,504 ÷ 26,584 = 6 + 0


=> 159,504 = 26,584 × 6


=> 159,504 is divisible by 26,584.


=> 159,504 is a multiple of 26,584.


The smallest multiple of 159,504 is the number itself: 159,504.


The least common multiple:
lcm (26,584; 159,504) = 159,504


lcm (26,584; 159,504) = 159,504 = 24 × 3 × 3,323
159,504 is a multiple of 26,584

Method 2. The prime factorization:

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


26,584 = 23 × 3,323
26,584 is not a prime number but a composite one.


159,504 = 24 × 3 × 3,323
159,504 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 (26,584; 159,504) = 24 × 3 × 3,323



lcm (26,584; 159,504) = 24 × 3 × 3,323 = 159,504
159,504 contains all the prime factors of the number 26,584

The final answer:
The least common multiple
lcm (26,584; 159,504) = 159,504 = 24 × 3 × 3,323
159,504 is divisible by 26,584. 159,504 is a multiple of 26,584.
159,504 contains all the prime factors of the number 26,584

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.


Other operations of this type:


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: the latest calculated

The LCM of 26,584 and 159,504 = ? May 27 06:18 UTC (GMT)
The LCM of 40,845 and 285,964 = ? May 27 06:18 UTC (GMT)
The LCM of 285 and 126 = ? May 27 06:18 UTC (GMT)
The LCM of 8 and 8,329 = ? May 27 06:18 UTC (GMT)
The LCM of 13 and 5,674 = ? May 27 06:18 UTC (GMT)
The LCM of 7,400 and 44,400 = ? May 27 06:18 UTC (GMT)
The LCM of 15 and 103 = ? May 27 06:18 UTC (GMT)
The LCM of 57 and 990 = ? May 27 06:18 UTC (GMT)
The LCM of 8 and 8,329 = ? May 27 06:17 UTC (GMT)
The LCM of 288 and 4 = ? May 27 06:17 UTC (GMT)
The LCM of 30,648 and 122,592 = ? May 27 06:17 UTC (GMT)
The LCM of 4,586 and 19 = ? May 27 06:17 UTC (GMT)
The LCM of 252,600 and 2,020,864 = ? May 27 06:17 UTC (GMT)
The least common multiple, LCM: the list of all the operations

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