The LCM (20,979 and 125,874) = ? Calculate the Least (the Lowest) Common Multiple, LCM, by Using Two Methods: 1) Numbers' Divisibility and 2) The Prime Factorization
The least common multiple
lcm (20,979; 125,874) = ?
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:
125,874 ÷ 20,979 = 6 + 0
⇒ 125,874 = 20,979 × 6
⇒ 125,874 is divisible by 20,979.
⇒ 125,874 is a multiple of 20,979.
The smallest multiple of 125,874 is the number itself: 125,874.
The least common multiple:
lcm (20,979; 125,874) = 125,874 = 2 × 35 × 7 × 37
125,874 is a multiple of 20,979
Scroll down for the 2nd method...
Method 2. The prime factorization:
The prime factorization of a number: finding the prime numbers that multiply together to make that number.
20,979 = 34 × 7 × 37
20,979 is not a prime number but a composite one.
125,874 = 2 × 35 × 7 × 37
125,874 is not a prime number but a composite one.
* Prime number: a natural number that is only divisible by 1 and itself. A prime number has exactly two factors: 1 and itself.
* Composite number: 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. If there are common prime factors then only the ones with the largest exponents are taken (the largest powers).
The least common multiple:
lcm (20,979; 125,874) = 2 × 35 × 7 × 37 = 125,874
125,874 contains all the prime factors of the number 20,979
Why is it useful to calculate the least common multiple?
In order to add, subtract or sort fractions with different denominators, we must make their denominators the same. An easy way is to calculate the least common multiple of all the denominators (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 similar operations with the least common multiple:
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.