Math Problem Statement
Calculate the least common multiple of 123456 and 987654.
Solution
To calculate the least common multiple (LCM) of two numbers, we use the relationship between the greatest common divisor (GCD) and the LCM:
Step 1: Find the GCD of 123456 and 987654.
Using the Euclidean algorithm, we can calculate the GCD.
So, the GCD of 123456 and 987654 is 6.
Step 2: Use the GCD to find the LCM.
Now, we can plug the values into the formula:
Calculating:
Thus, the least common multiple (LCM) of 123456 and 987654 is 20,321,968,704.
Would you like more details on this? Here are some related questions:
- How does the Euclidean algorithm work in GCD calculations?
- What are the practical applications of finding the LCM?
- What is the difference between the GCD and LCM of two numbers?
- How can we apply the prime factorization method to find LCM?
- How does the LCM formula relate to divisibility rules?
Tip: When two numbers are relatively prime (i.e., GCD = 1), their LCM is simply their product!
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Math Problem Analysis
Mathematical Concepts
Number Theory
LCM
GCD
Formulas
LCM(a, b) = |a × b| / GCD(a, b)
Euclidean Algorithm for GCD
Theorems
Euclidean Algorithm
Suitable Grade Level
Grades 10-12