Least Common Multiple (LCM) of 185 and 67
The least common multiple (LCM) of 185 and 67 is 12395.
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 67?
First, calculate the GCD of 185 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 67 = 2 remainder 51 |
| 2 | 67 ÷ 51 = 1 remainder 16 |
| 3 | 51 ÷ 16 = 3 remainder 3 |
| 4 | 16 ÷ 3 = 5 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 42 | 3738 |
| 192 and 10 | 960 |
| 167 and 112 | 18704 |
| 107 and 186 | 19902 |
| 127 and 43 | 5461 |