Least Common Multiple (LCM) of 67 and 185
The least common multiple (LCM) of 67 and 185 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 67 and 185?
First, calculate the GCD of 67 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 185 = 0 remainder 67 |
| 2 | 185 ÷ 67 = 2 remainder 51 |
| 3 | 67 ÷ 51 = 1 remainder 16 |
| 4 | 51 ÷ 16 = 3 remainder 3 |
| 5 | 16 ÷ 3 = 5 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 187 | 5984 |
| 138 and 23 | 138 |
| 54 and 27 | 54 |
| 138 and 143 | 19734 |
| 96 and 84 | 672 |