Least Common Multiple (LCM) of 186 and 103
The least common multiple (LCM) of 186 and 103 is 19158.
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 103?
First, calculate the GCD of 186 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 103 = 1 remainder 83 |
| 2 | 103 ÷ 83 = 1 remainder 20 |
| 3 | 83 ÷ 20 = 4 remainder 3 |
| 4 | 20 ÷ 3 = 6 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 12 | 300 |
| 116 and 57 | 6612 |
| 20 and 76 | 380 |
| 171 and 169 | 28899 |
| 138 and 76 | 5244 |