Least Common Multiple (LCM) of 125 and 189
The least common multiple (LCM) of 125 and 189 is 23625.
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 189?
First, calculate the GCD of 125 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 189 = 0 remainder 125 |
| 2 | 189 ÷ 125 = 1 remainder 64 |
| 3 | 125 ÷ 64 = 1 remainder 61 |
| 4 | 64 ÷ 61 = 1 remainder 3 |
| 5 | 61 ÷ 3 = 20 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 36 | 1980 |
| 99 and 63 | 693 |
| 124 and 122 | 7564 |
| 67 and 140 | 9380 |
| 184 and 138 | 552 |