Least common multiple
The least common multiple (LCM) of two or more numbers is the smallest multiple that is evenly divisible by each of the numbers
The least common multiple (LCM) of two or more numbers is the smallest multiple that is evenly divisible by each of the numbers. In other words, it is the smallest number that all given numbers can divide into without leaving a remainder.
To find the LCM, you can follow these steps:
Step 1: Prime Factorization
Start by finding the prime factorization of each given number. Prime factorization is the process of breaking down a number into its prime factors, which are the numbers that can only be divided evenly by themselves and 1.
For example, let’s find the LCM of 12 and 18.
The prime factorization of 12 is: 2^2 * 3
The prime factorization of 18 is: 2 * 3^2
Step 2: Identify Common Factors
Next, list down all the distinct prime factors from both numbers. In this case, we have 2, 2, 3, and 3.
Step 3: Determine Power of Each Factor
For each prime factor, write down the highest power that appears among the two numbers. In this case, we have 2^2 and 3^2.
Step 4: Multiply the Factors
Multiply all the distinct prime factors together, using the highest powers determined in the previous step.
2^2 * 3^2 = 4 * 9 = 36
Therefore, the LCM of 12 and 18 is 36.
In general, for multiple numbers, the steps remain the same. Simply list down the prime factors of all numbers, identify common factors, determine the power of each factor, and multiply them together to find the LCM.
I hope this explanation helps! Let me know if you have any further questions.
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