Least Common Multiple (LCM) of 125 and 188
The least common multiple (LCM) of 125 and 188 is 23500.
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 125 and 188?
First, calculate the GCD of 125 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 188 = 0 remainder 125 |
| 2 | 188 ÷ 125 = 1 remainder 63 |
| 3 | 125 ÷ 63 = 1 remainder 62 |
| 4 | 63 ÷ 62 = 1 remainder 1 |
| 5 | 62 ÷ 1 = 62 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 198 | 21186 |
| 126 and 54 | 378 |
| 132 and 150 | 3300 |
| 46 and 21 | 966 |
| 20 and 116 | 580 |