Least Common Multiple (LCM) of 185 and 34
The least common multiple (LCM) of 185 and 34 is 6290.
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 34?
First, calculate the GCD of 185 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 34 = 5 remainder 15 |
| 2 | 34 ÷ 15 = 2 remainder 4 |
| 3 | 15 ÷ 4 = 3 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 21 | 357 |
| 147 and 47 | 6909 |
| 127 and 94 | 11938 |
| 168 and 173 | 29064 |
| 193 and 54 | 10422 |