Least Common Multiple (LCM) of 186 and 109
The least common multiple (LCM) of 186 and 109 is 20274.
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 109?
First, calculate the GCD of 186 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 109 = 1 remainder 77 |
| 2 | 109 ÷ 77 = 1 remainder 32 |
| 3 | 77 ÷ 32 = 2 remainder 13 |
| 4 | 32 ÷ 13 = 2 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 188 | 4324 |
| 140 and 151 | 21140 |
| 198 and 69 | 4554 |
| 39 and 16 | 624 |
| 178 and 78 | 6942 |