Least Common Multiple (LCM) of 89 and 193
The least common multiple (LCM) of 89 and 193 is 17177.
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 89 and 193?
First, calculate the GCD of 89 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 193 = 0 remainder 89 |
| 2 | 193 ÷ 89 = 2 remainder 15 |
| 3 | 89 ÷ 15 = 5 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 197 | 3743 |
| 112 and 39 | 4368 |
| 192 and 141 | 9024 |
| 105 and 83 | 8715 |
| 129 and 185 | 23865 |