Least Common Multiple (LCM) of 186 and 107
The least common multiple (LCM) of 186 and 107 is 19902.
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 107?
First, calculate the GCD of 186 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 107 = 1 remainder 79 |
| 2 | 107 ÷ 79 = 1 remainder 28 |
| 3 | 79 ÷ 28 = 2 remainder 23 |
| 4 | 28 ÷ 23 = 1 remainder 5 |
| 5 | 23 ÷ 5 = 4 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 109 | 109 |
| 123 and 81 | 3321 |
| 182 and 137 | 24934 |
| 134 and 156 | 10452 |
| 176 and 186 | 16368 |