LCM (6,163; 31) = ? Calculate the least common multiple, LCM, by two methods: 1) The prime factorization of the numbers and 2) The Euclidean algorithm

lcm (6,163; 31) = ?

Method 1. The prime factorization:

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


6,163 is a prime number, it cannot be broken down into other prime factors.


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


* 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 (6,163; 31) = 31 × 6,163



lcm (6,163; 31) = 31 × 6,163 = 191,053
The two numbers have no prime factors in common:
191,053 = 6,163 × 31

Method 2. The Euclidean Algorithm:

Calculate the greatest (highest) common factor (divisor):

This algorithm involves the process of dividing numbers and calculating the remainders.


'a' and 'b' are the two natural numbers, 'a' >= 'b'.


Divide 'a' by 'b' and get the remainder of the operation, 'r'.


If 'r' = 0, STOP. 'b' = the gcf (hcf, gcd) of 'a' and 'b'.


Else: Replace ('a' by 'b') and ('b' by 'r'). Return to the step above.



Step 1. Divide the larger number by the smaller one:
6,163 ÷ 31 = 198 + 25
Step 2. Divide the smaller number by the above operation's remainder:
31 ÷ 25 = 1 + 6
Step 3. Divide the remainder of the step 1 by the remainder of the step 2:
25 ÷ 6 = 4 + 1
Step 4. Divide the remainder of the step 2 by the remainder of the step 3:
6 ÷ 1 = 6 + 0
At this step, the remainder is zero, so we stop:
1 is the number we were looking for - the last non-zero remainder.
This is the greatest (highest) common factor (divisor).


The greatest (highest) common factor (divisor):
gcf, hcf, gcd (6,163; 31) = 1


Calculate the least common multiple:

The least common multiple, Formula:

lcm (a; b) = (a × b) / gcf, hcf, gcd (a; b)


lcm (6,163; 31) =


(6,163 × 31) / gcf, hcf, gcd (6,163; 31) =


191,053 / 1 =


191,053


lcm (6,163; 31) = 191,053 = 31 × 6,163

The final answer:
The least common multiple
lcm (6,163; 31) = 191,053 = 31 × 6,163
The two numbers have no prime factors in common:
191,053 = 6,163 × 31

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 6,163 and 31 = ? May 24 21:16 UTC (GMT)
The LCM of 441 and 225 = ? May 24 21:16 UTC (GMT)
The LCM of 4 and 8 = ? May 24 21:15 UTC (GMT)
The LCM of 1,035 and 36 = ? May 24 21:15 UTC (GMT)
The LCM of 22 and 600 = ? May 24 21:15 UTC (GMT)
The LCM of 948 and 1,536 = ? May 24 21:15 UTC (GMT)
The LCM of 5,862 and 512 = ? May 24 21:15 UTC (GMT)
The LCM of 10,520 and 84,224 = ? May 24 21:15 UTC (GMT)
The LCM of 180,252 and 594 = ? May 24 21:15 UTC (GMT)
The LCM of 571 and 6 = ? May 24 21:15 UTC (GMT)
The LCM of 716 and 78 = ? May 24 21:15 UTC (GMT)
The LCM of 89 and 116 = ? May 24 21:15 UTC (GMT)
The LCM of 120,148,200 and 120,148,200 = ? May 24 21:15 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