Least Common Multiple (LCM) of 185 and 68
The least common multiple (LCM) of 185 and 68 is 12580.
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 185 and 68?
First, calculate the GCD of 185 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 68 = 2 remainder 49 |
| 2 | 68 ÷ 49 = 1 remainder 19 |
| 3 | 49 ÷ 19 = 2 remainder 11 |
| 4 | 19 ÷ 11 = 1 remainder 8 |
| 5 | 11 ÷ 8 = 1 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 71 | 13845 |
| 103 and 30 | 3090 |
| 138 and 186 | 4278 |
| 31 and 144 | 4464 |
| 35 and 185 | 1295 |