Least Common Multiple (LCM) of 68 and 186
The least common multiple (LCM) of 68 and 186 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 68 and 186?
First, calculate the GCD of 68 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 186 = 0 remainder 68 |
| 2 | 186 ÷ 68 = 2 remainder 50 |
| 3 | 68 ÷ 50 = 1 remainder 18 |
| 4 | 50 ÷ 18 = 2 remainder 14 |
| 5 | 18 ÷ 14 = 1 remainder 4 |
| 6 | 14 ÷ 4 = 3 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 97 | 1940 |
| 105 and 107 | 11235 |
| 136 and 99 | 13464 |
| 64 and 83 | 5312 |
| 124 and 179 | 22196 |