Least Common Multiple (LCM) of 186 and 195
The least common multiple (LCM) of 186 and 195 is 12090.
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 186 and 195?
First, calculate the GCD of 186 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 195 = 0 remainder 186 |
| 2 | 195 ÷ 186 = 1 remainder 9 |
| 3 | 186 ÷ 9 = 20 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 10 | 30 |
| 105 and 56 | 840 |
| 123 and 110 | 13530 |
| 132 and 129 | 5676 |
| 178 and 80 | 7120 |