Least Common Multiple (LCM) of 123 and 188
The least common multiple (LCM) of 123 and 188 is 23124.
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 188?
First, calculate the GCD of 123 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 188 = 0 remainder 123 |
| 2 | 188 ÷ 123 = 1 remainder 65 |
| 3 | 123 ÷ 65 = 1 remainder 58 |
| 4 | 65 ÷ 58 = 1 remainder 7 |
| 5 | 58 ÷ 7 = 8 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 196 | 588 |
| 135 and 30 | 270 |
| 150 and 194 | 14550 |
| 71 and 173 | 12283 |
| 183 and 41 | 7503 |