How to Find LCM of 2 Numbers?
To find the LCM of two numbers, identify their prime factors and calculate the product of the highest powers of these factors.
Explanation:
What is LCM?
LCM stands for “Least Common Multiple.” It refers to the smallest positive integer that is divisible by two or more given integers without leaving a remainder. In other words, the LCM is the smallest number that is a multiple of each of the given numbers.
Step-by-Step Method
Step 1: Prime Factorization: Break down each number into its prime factors.
Step 2: Identify Common Factors: Look for the prime factors they share.
Step 3: Select Highest Powers: Pick the highest occurrences of each shared prime factor.
Step 4: Multiply: Multiply those highest powers together.
Let’s apply this method to find the LCM of 12 and 18:
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Prime Factorization:
- 12 = 2 × 2 × 3
- 18 = 2 × 3 × 3
- Identify Common Factors: Both have 2 and 3 as prime factors.
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Select Highest Powers:
- 2 occurs twice in 12, and once in 18. So, we choose it twice.
- 3 occurs once in 12, twice in 18. We pick it twice.
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Multiply:
- LCM = 2^2 × 3^2 = 4 × 9 = 36
Hence, the LCM of 12 and 18 is 36.
Conclusion
In conclusion, mastering the method for finding the LCM of two numbers empowers individuals to solve mathematical problems efficiently and accurately. By understanding the principles of prime factorization and highest power selection, one can confidently determine the LCM and apply it in various mathematical contexts.