Least Common Multiple (LCM) of 123 and 185
The least common multiple (LCM) of 123 and 185 is 22755.
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 185?
First, calculate the GCD of 123 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 185 = 0 remainder 123 |
| 2 | 185 ÷ 123 = 1 remainder 62 |
| 3 | 123 ÷ 62 = 1 remainder 61 |
| 4 | 62 ÷ 61 = 1 remainder 1 |
| 5 | 61 ÷ 1 = 61 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 89 and 198 | 17622 |
| 74 and 63 | 4662 |
| 18 and 78 | 234 |
| 149 and 191 | 28459 |
| 17 and 45 | 765 |