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Lowest Common Multiple (LCM) to a 6th-grade.
Let’s explain the concept of the Lowest Common Multiple (LCM) to a 6th-grade level.
The Lowest Common Multiple (LCM) is the smallest positive number that is divisible by two or more given numbers. It is often used when dealing with fractions, simplifying fractions, or solving problems involving multiple numbers or quantities.
To find the LCM of two or more numbers, we follow these steps:
Step 1: Start by listing the multiples of each number.
For example, let’s find the LCM of 4 and 6.
Multiples of 4: 4, 8, 12, 16, 20, 24, …
Multiples of 6: 6, 12, 18, 24, 30, 36, …
Step 2: Identify the smallest common multiple in the lists.
In this case, we see that 12 is the smallest common multiple of 4 and 6.
Therefore, the LCM of 4 and 6 is 12.
The LCM can also be found using prime factorization. Here’s an example:
Let’s find the LCM of 8 and 12.
Step 1: Write the prime factorization of each number.
8 = 2 × 2 × 2
12 = 2 × 2 × 3
Step 2: Take the highest power of each prime factor.
2² × 3
Step 3: Multiply the highest powers together.
2² × 3 = 4 × 3 = 12
Therefore, the LCM of 8 and 12 is 12.
The LCM helps us in various mathematical operations, such as adding or subtracting fractions with different denominators, finding a common time or interval, or solving problems that involve multiple quantities or events occurring simultaneously.
In summary, the LCM is the smallest positive number that is divisible by two or more given numbers. It can be found by listing multiples or using prime factorization. The LCM is useful in many mathematical calculations and problem-solving scenarios.
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