Least Common Multiple (LCM) of 125 and 180
The least common multiple (LCM) of 125 and 180 is 4500.
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 180?
First, calculate the GCD of 125 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 180 = 0 remainder 125 |
| 2 | 180 ÷ 125 = 1 remainder 55 |
| 3 | 125 ÷ 55 = 2 remainder 15 |
| 4 | 55 ÷ 15 = 3 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 69 | 1380 |
| 185 and 164 | 30340 |
| 75 and 116 | 8700 |
| 175 and 120 | 4200 |
| 136 and 196 | 6664 |