Least Common Multiple (LCM) of 107 and 185
The least common multiple (LCM) of 107 and 185 is 19795.
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 107 and 185?
First, calculate the GCD of 107 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 185 = 0 remainder 107 |
| 2 | 185 ÷ 107 = 1 remainder 78 |
| 3 | 107 ÷ 78 = 1 remainder 29 |
| 4 | 78 ÷ 29 = 2 remainder 20 |
| 5 | 29 ÷ 20 = 1 remainder 9 |
| 6 | 20 ÷ 9 = 2 remainder 2 |
| 7 | 9 ÷ 2 = 4 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 152 | 1216 |
| 178 and 140 | 12460 |
| 77 and 36 | 2772 |
| 68 and 97 | 6596 |
| 197 and 186 | 36642 |