Least Common Multiple (LCM) of 67 and 194
The least common multiple (LCM) of 67 and 194 is 12998.
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 194?
First, calculate the GCD of 67 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 194 = 0 remainder 67 |
| 2 | 194 ÷ 67 = 2 remainder 60 |
| 3 | 67 ÷ 60 = 1 remainder 7 |
| 4 | 60 ÷ 7 = 8 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 39 | 2340 |
| 90 and 142 | 6390 |
| 106 and 158 | 8374 |
| 70 and 110 | 770 |
| 107 and 153 | 16371 |