Least Common Multiple (LCM) of 180 and 125
The least common multiple (LCM) of 180 and 125 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 180 and 125?
First, calculate the GCD of 180 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 125 = 1 remainder 55 |
| 2 | 125 ÷ 55 = 2 remainder 15 |
| 3 | 55 ÷ 15 = 3 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 152 and 32 | 608 |
| 84 and 93 | 2604 |
| 128 and 31 | 3968 |
| 36 and 48 | 144 |
| 59 and 199 | 11741 |