Least Common Multiple (LCM) of 125 and 36
The least common multiple (LCM) of 125 and 36 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 36?
First, calculate the GCD of 125 and 36 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 36 = 3 remainder 17 |
| 2 | 36 ÷ 17 = 2 remainder 2 |
| 3 | 17 ÷ 2 = 8 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 12 | 60 |
| 138 and 188 | 12972 |
| 36 and 60 | 180 |
| 177 and 199 | 35223 |
| 171 and 53 | 9063 |