Least Common Multiple (LCM) of 68 and 193
The least common multiple (LCM) of 68 and 193 is 13124.
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 68 and 193?
First, calculate the GCD of 68 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 193 = 0 remainder 68 |
| 2 | 193 ÷ 68 = 2 remainder 57 |
| 3 | 68 ÷ 57 = 1 remainder 11 |
| 4 | 57 ÷ 11 = 5 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 42 | 1386 |
| 87 and 63 | 1827 |
| 107 and 24 | 2568 |
| 104 and 22 | 1144 |
| 134 and 37 | 4958 |