The LCM (16 and 80) = ? 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 (16; 80) = ?
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:
80 ÷ 16 = 5 + 0
⇒ 80 = 16 × 5
⇒ 80 is divisible by 16.
⇒ 80 is a multiple of 16.
The smallest multiple of 80 is the number itself: 80.
The least common multiple:
lcm (16; 80) = 80 = 24 × 5
80 is a multiple of 16
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.
16 = 24
16 is not a prime number but a composite one.
80 = 24 × 5
80 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 (16; 80) = 24 × 5 = 80
80 contains all the prime factors of the number 16
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.