How can I decide if I'm going to solve a problem using common multiple or common factors. When do we use common multiple or common factors in problem solving?
To determine whether to use common multiples or common factors in problem solving, you need to understand the nature of the problem and what you are trying to find.
Common multiples are used when you need to find a number that is divisible by all given numbers. To find common multiples, you can start by listing the multiples of each number until you find a number that is a multiple of all the given numbers. This method is commonly used in problems involving finding the least common multiple (LCM) of two or more numbers.
Common factors, on the other hand, are used when you need to find numbers that can divide evenly into all given numbers. To find common factors, you can start by finding the factors of each number and identifying the numbers that are common to all given numbers. This method is frequently used in problems involving finding the greatest common factor (GCF) of two or more numbers.
Here's an example to illustrate the difference:
Let's say you have a problem where you need to find the smallest number that is evenly divisible by 6, 8, and 12. In this case, you would use common multiples to find the least common multiple (LCM) of these numbers. You would list the multiples of each number until you find a number that is divisible by all three. In this case, the LCM would be 24.
However, if you had a problem where you needed to find the largest number that can evenly divide into 24, 36, and 48, you would use common factors to find the greatest common factor (GCF) of these numbers. You would list the factors of each number and identify the numbers that are common to all three. In this case, the GCF would be 12.
In summary, the choice between using common multiples or common factors in problem solving depends on the specific problem and what you are trying to find. If you need a number that is divisible by all given numbers, use common multiples (LCM). If you need a number that can divide evenly into all given numbers, use common factors (GCF).