Least Common Multiple (LCM) of 125 and 195
The least common multiple (LCM) of 125 and 195 is 4875.
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 195?
First, calculate the GCD of 125 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 195 = 0 remainder 125 |
| 2 | 195 ÷ 125 = 1 remainder 70 |
| 3 | 125 ÷ 70 = 1 remainder 55 |
| 4 | 70 ÷ 55 = 1 remainder 15 |
| 5 | 55 ÷ 15 = 3 remainder 10 |
| 6 | 15 ÷ 10 = 1 remainder 5 |
| 7 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 189 | 35910 |
| 104 and 111 | 11544 |
| 105 and 47 | 4935 |
| 104 and 172 | 4472 |
| 31 and 150 | 4650 |