Least Common Multiple (LCM) of 114 and 195
The least common multiple (LCM) of 114 and 195 is 7410.
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 114 and 195?
First, calculate the GCD of 114 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 195 = 0 remainder 114 |
| 2 | 195 ÷ 114 = 1 remainder 81 |
| 3 | 114 ÷ 81 = 1 remainder 33 |
| 4 | 81 ÷ 33 = 2 remainder 15 |
| 5 | 33 ÷ 15 = 2 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 129 | 6708 |
| 39 and 180 | 2340 |
| 137 and 89 | 12193 |
| 188 and 156 | 7332 |
| 176 and 60 | 2640 |