Least Common Multiple (LCM) of 186 and 68
The least common multiple (LCM) of 186 and 68 is 6324.
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 68?
First, calculate the GCD of 186 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 68 = 2 remainder 50 |
| 2 | 68 ÷ 50 = 1 remainder 18 |
| 3 | 50 ÷ 18 = 2 remainder 14 |
| 4 | 18 ÷ 14 = 1 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 177 | 5841 |
| 74 and 99 | 7326 |
| 137 and 191 | 26167 |
| 13 and 129 | 1677 |
| 153 and 14 | 2142 |