Least Common Multiple (LCM) of 102 and 186
The least common multiple (LCM) of 102 and 186 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 102 and 186?
First, calculate the GCD of 102 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 186 = 0 remainder 102 |
| 2 | 186 ÷ 102 = 1 remainder 84 |
| 3 | 102 ÷ 84 = 1 remainder 18 |
| 4 | 84 ÷ 18 = 4 remainder 12 |
| 5 | 18 ÷ 12 = 1 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 46 | 6946 |
| 145 and 127 | 18415 |
| 164 and 32 | 1312 |
| 78 and 180 | 2340 |
| 60 and 39 | 780 |