Least Common Multiple (LCM) of 101 and 186
The least common multiple (LCM) of 101 and 186 is 18786.
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 101 and 186?
First, calculate the GCD of 101 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 186 = 0 remainder 101 |
| 2 | 186 ÷ 101 = 1 remainder 85 |
| 3 | 101 ÷ 85 = 1 remainder 16 |
| 4 | 85 ÷ 16 = 5 remainder 5 |
| 5 | 16 ÷ 5 = 3 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 114 | 10374 |
| 14 and 71 | 994 |
| 84 and 190 | 7980 |
| 102 and 12 | 204 |
| 14 and 103 | 1442 |