Least Common Multiple (LCM) of 193 and 67
The least common multiple (LCM) of 193 and 67 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 193 and 67?
First, calculate the GCD of 193 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 67 = 2 remainder 59 |
| 2 | 67 ÷ 59 = 1 remainder 8 |
| 3 | 59 ÷ 8 = 7 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 20 | 2780 |
| 110 and 144 | 7920 |
| 199 and 17 | 3383 |
| 69 and 92 | 276 |
| 175 and 83 | 14525 |