Least Common Multiple (LCM) of 67 and 193
The least common multiple (LCM) of 67 and 193 is 12931.
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 193?
First, calculate the GCD of 67 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 193 = 0 remainder 67 |
| 2 | 193 ÷ 67 = 2 remainder 59 |
| 3 | 67 ÷ 59 = 1 remainder 8 |
| 4 | 59 ÷ 8 = 7 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 140 | 5740 |
| 97 and 169 | 16393 |
| 129 and 78 | 3354 |
| 59 and 12 | 708 |
| 160 and 107 | 17120 |