Least Common Multiple (LCM) of 89 and 194
The least common multiple (LCM) of 89 and 194 is 17266.
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 194?
First, calculate the GCD of 89 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 194 = 0 remainder 89 |
| 2 | 194 ÷ 89 = 2 remainder 16 |
| 3 | 89 ÷ 16 = 5 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 127 and 29 | 3683 |
| 140 and 64 | 2240 |
| 143 and 101 | 14443 |
| 97 and 67 | 6499 |
| 135 and 115 | 3105 |