Least Common Multiple (LCM) of 195 and 125
The least common multiple (LCM) of 195 and 125 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 195 and 125?
First, calculate the GCD of 195 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 125 = 1 remainder 70 |
| 2 | 125 ÷ 70 = 1 remainder 55 |
| 3 | 70 ÷ 55 = 1 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 |
|---|---|
| 142 and 153 | 21726 |
| 62 and 61 | 3782 |
| 55 and 109 | 5995 |
| 116 and 17 | 1972 |
| 120 and 123 | 4920 |