Least Common Multiple (LCM) of 186 and 108
The least common multiple (LCM) of 186 and 108 is 3348.
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 108?
First, calculate the GCD of 186 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 108 = 1 remainder 78 |
| 2 | 108 ÷ 78 = 1 remainder 30 |
| 3 | 78 ÷ 30 = 2 remainder 18 |
| 4 | 30 ÷ 18 = 1 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 38 | 3800 |
| 165 and 58 | 9570 |
| 158 and 186 | 14694 |
| 30 and 181 | 5430 |
| 98 and 60 | 2940 |