Calculate the least common multiple of 123456 and 987654.



To calculate the least common multiple (LCM) of two numbers, we use the relationship between the greatest common divisor (GCD) and the LCM:

\[
\text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)}
\]

### Step 1: Find the GCD of 123456 and 987654.

Using the Euclidean algorithm, we can calculate the GCD.

- \(987654 \div 123456 = 8 \text{ remainder } 6\)
- \(123456 \div 6 = 20576 \text{ remainder } 0\)

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:

\[
\text{LCM}(123456, 987654) = \frac{123456 \times 987654}{6}
\]

Calculating:

\[
123456 \times 987654 = 121931812224
\]

\[
\frac{121931812224}{6} = 20321968704
\]

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:

1. How does the Euclidean algorithm work in GCD calculations?
2. What are the practical applications of finding the LCM?
3. What is the difference between the GCD and LCM of two numbers?
4. How can we apply the prime factorization method to find LCM?
5. 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!

Calculate the least common multiple of 123456 and 987654.

Discover how to calculate the least common multiple (LCM) of 123456 and 987654 using the relationship between LCM and GCD. This detailed solution walks through applying the Euclidean algorithm to find the GCD and then calculating the LCM. Suitable for Grades 10-12.

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