MÚLTIPLO COMUM e MÁXIMO DIVISOR COMUM | MMC e MDC - RESUMÃO -

Summary

This video tutorial explains the concepts of MMC (Least Common Multiple) and MDC (Greatest Common Divisor) using practical examples with the numbers 15 and 18. The presenter walks through the step-by-step process for finding both the MMC and MDC, including how to apply prime factorization and identify the results. Viewers are shown the differences between MMC and MDC and given tips for identifying which method to use in word problems. The tutorial also emphasizes the importance of practice and provides additional lessons for further understanding and exercises.

Takeaways

• 😀 MMC (Least Common Multiple) is the smallest multiple that two numbers share in common.
• 😀 MDC (Greatest Common Divisor) is the largest number that divides both numbers without leaving a remainder.
• 😀 To find the MMC, multiply all the prime factors together once the division process is completed.
• 😀 For MDC, only circle the prime numbers that divide both numbers at each step of division.
• 😀 The process for finding MMC involves checking the multiplication tables of the numbers for the first common multiple.
• 😀 The MDC process involves finding the largest common divisor by dividing by prime numbers until the numbers are reduced to 1.
• 😀 When solving MMC, it’s important to think of prime divisors and ensure the number is divisible by both numbers.
• 😀 If no number is circled in the MDC process, the result is 1, indicating there is no common divisor other than 1.
• 😀 A helpful tip for MMC is to focus on the first multiple shared by both numbers when using multiplication tables.
• 😀 For word problems involving syncing up events, use MMC. For problems involving dividing into parts, use MDC.
• 😀 Consistent practice with exercises is important to master the application of MMC and MDC in different problem scenarios.

Q & A

What is the difference between MMC and MDC?

MMC (Mínimo Múltiplo Comum) refers to the smallest common multiple between two numbers, while MDC (Máximo Divisor Comum) refers to the largest common divisor of those two numbers.

How is MMC calculated?

To calculate the MMC, you find the prime factors of each number, then multiply them together. For 15 and 18, the MMC is calculated as 3 × 3 × 2 × 5 = 90.

What is the first step in calculating the MDC of two numbers?

The first step is to divide both numbers by prime numbers, checking which primes divide both numbers. For example, for 15 and 18, you start with 3.

Why do you need to multiply all the prime factors together in the MMC calculation?

You multiply all the prime factors together because the MMC is the smallest number that contains all the prime factors of both numbers, ensuring it’s a common multiple.

How do you identify the MDC of two numbers?

To identify the MDC, you look for common prime factors during the division process and multiply those factors. In the case of 15 and 18, the common prime factor is 3.

Can you start with any prime number when calculating the MDC?

Yes, you can start with any prime number. However, it’s important to check which primes divide both numbers. In the case of 15 and 18, starting with 3 works, but starting with 2 would also work in some cases.

What happens if no prime factors are common when calculating the MDC?

If no prime factors are common, the MDC is 1, meaning the two numbers have no common divisors other than 1.

What would you do if multiple prime factors were circled during the MDC process?

If multiple prime factors are circled, you multiply them together to find the MDC. For example, if both 2 and 3 were circled, you would calculate 2 × 3 = 6.

How do you know when to use MMC or MDC in a problem?

You use MMC when the problem refers to finding a common multiple, such as when trying to find when two events will meet again. You use MDC when the problem involves dividing or cutting something into the largest possible groups.

What should you do if you're not sure whether a problem requires MMC or MDC?

If you're unsure, look at the context of the problem. If it’s about combining or finding a shared time or quantity, it's likely MMC. If it’s about dividing or grouping, then it's MDC.