Least Common Multiple (LCM) of 123 and 68
The least common multiple (LCM) of 123 and 68 is 8364.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 123 and 68?
First, calculate the GCD of 123 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 68 = 1 remainder 55 |
| 2 | 68 ÷ 55 = 1 remainder 13 |
| 3 | 55 ÷ 13 = 4 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 75 | 2775 |
| 123 and 81 | 3321 |
| 45 and 111 | 1665 |
| 32 and 43 | 1376 |
| 111 and 68 | 7548 |