Least Common Multiple (LCM) of 186 and 102
The least common multiple (LCM) of 186 and 102 is 3162.
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 102?
First, calculate the GCD of 186 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 102 = 1 remainder 84 |
| 2 | 102 ÷ 84 = 1 remainder 18 |
| 3 | 84 ÷ 18 = 4 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 69 | 6900 |
| 126 and 42 | 126 |
| 157 and 41 | 6437 |
| 183 and 90 | 5490 |
| 150 and 83 | 12450 |