Least Common Multiple (LCM) of 186 and 50
The least common multiple (LCM) of 186 and 50 is 4650.
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 50?
First, calculate the GCD of 186 and 50 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 50 = 3 remainder 36 |
| 2 | 50 ÷ 36 = 1 remainder 14 |
| 3 | 36 ÷ 14 = 2 remainder 8 |
| 4 | 14 ÷ 8 = 1 remainder 6 |
| 5 | 8 ÷ 6 = 1 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 126 | 2016 |
| 77 and 163 | 12551 |
| 12 and 188 | 564 |
| 112 and 63 | 1008 |
| 29 and 61 | 1769 |