Least Common Multiple (LCM) of 193 and 114
The least common multiple (LCM) of 193 and 114 is 22002.
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 114?
First, calculate the GCD of 193 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 193 ÷ 114 = 1 remainder 79 |
| 2 | 114 ÷ 79 = 1 remainder 35 |
| 3 | 79 ÷ 35 = 2 remainder 9 |
| 4 | 35 ÷ 9 = 3 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 115 | 1150 |
| 157 and 104 | 16328 |
| 194 and 22 | 2134 |
| 91 and 188 | 17108 |
| 199 and 171 | 34029 |