Least Common Multiple (LCM) of 57 and 195
The least common multiple (LCM) of 57 and 195 is 3705.
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 57 and 195?
First, calculate the GCD of 57 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 57 ÷ 195 = 0 remainder 57 |
| 2 | 195 ÷ 57 = 3 remainder 24 |
| 3 | 57 ÷ 24 = 2 remainder 9 |
| 4 | 24 ÷ 9 = 2 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 134 | 6834 |
| 60 and 95 | 1140 |
| 34 and 65 | 2210 |
| 104 and 125 | 13000 |
| 105 and 184 | 19320 |