MMC (Least Common Multiple) and MDC (Least Common Divisor) are mathematical rules linked, respectively, to the common multiple and the common divisor of two or more numbers.
They are tools used to facilitate the solving of problems and equations.
The MMC is the smallest value that can be multiple of two or more numbers. The MDC is the biggest number that can divide multiple numbers at the same time.
What is a divisor number and a multiple number?
To better understand the concepts of MMC and MDC, it is necessary to know what is a divisor number and what is a multiple number.
A number is called divider when the count of its division by another yields a whole number.
Example: the number 36 can be divided by: 1, 2, 3, 6, 12, 18 and 36.
already the numbers multiples are the numbers that result from a multiplication made between a chosen number and any other value.
See the example of multiples of number 3.
| multiples | |
| 3 | 3 (3 x 1), 6 (3 x 2), 9 (3 x 3), 12 (3 x 4), 15 (3 x 5), 18 (3 x 6), 21 (3 x 7). . |
MMC
The Least Common Multiple (MMC) calculus serves to facilitate the solving of mathematical problems involving two or more numbers. The MMC will be the smallest common multiple found between two or more numbers.
See in this example the common multiples between 2 and 4.
| Multiples of 2 | 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20... |
| Multiples of 4 | 0, 4, 8, 12, 16, 20, 24, 28, 32, 36... |
| Common multiple numbers between 2 and 4 | 0, 4, 12... |
How to calculate MMC
To determine the least common multiple between two or more numbers, you need to follow two steps:
- Find out what the multiples of numbers are.
- Check which is the smallest number that is a multiple of all.
To better understand, see this example of calculating the MMC between 4 and 6.
| multiples | |
| 4 | 4, 8, 12, 16, 20... |
| 6 | 6,12, 18, 24, 30... |
| MMC (4.6) | 12 |
In this example the smallest number that is a multiple of 4 and 6 is 12.
MDC
The greatest common divisor (MDC) is the largest number that divides several other numbers at the same time.
How to calculate the MDC
To calculate the greatest common divisor it is necessary to decompose the numbers through factorization.
- Decompose all the numbers.
- Find common numbers across all decompositions.
- The MDC will be the value of the multiplication of the common numbers.
See the example of calculating the MDC between the numbers 20 and 50.
| Decomposition | |
| 20 | 2 x 3 x 5 |
| 50 | 2 x 5 x5 |
| MDC (20.50) | 10 (2 x 5) |
The MDC result between 20 and 50 is 10. To know the MDC result, just multiply the common divisors (2 and 5).
Differences between MMC and MDC
The ways to calculate MMC and MDC have some similarities. Therefore, it is important to pay attention to don't confuse the concepts.
The easiest way to understand the differences between them is to know the practical applications of each.
MMC
The first step is to see if the problem requires finding a minimum number or multiple that simplifies resolution. In these cases the MMC must be used.
It can be used, for example, to solve equations that have fractions with different denominators, as the least common multiple facilitates the resolution of this type of problem.
MMC can also be used to compare different fractions to determine if they are equivalent.
MDC
The MDC should be used when the problem involves some question about division calculations.
For example, MDC can be used to solve problems where you need to determine the largest or smallest size of something.
See also the meanings of Arithmetic and Arithmetic Progression.
