Least Common Multiple (LCM) of 105 and 186
The least common multiple (LCM) of 105 and 186 is 6510.
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 105 and 186?
First, calculate the GCD of 105 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 186 = 0 remainder 105 |
| 2 | 186 ÷ 105 = 1 remainder 81 |
| 3 | 105 ÷ 81 = 1 remainder 24 |
| 4 | 81 ÷ 24 = 3 remainder 9 |
| 5 | 24 ÷ 9 = 2 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 30 | 30 |
| 12 and 125 | 1500 |
| 105 and 164 | 17220 |
| 87 and 55 | 4785 |
| 143 and 51 | 7293 |