Least Common Multiple (LCM) of 89 and 191
The least common multiple (LCM) of 89 and 191 is 16999.
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 191?
First, calculate the GCD of 89 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 191 = 0 remainder 89 |
| 2 | 191 ÷ 89 = 2 remainder 13 |
| 3 | 89 ÷ 13 = 6 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 114 | 2394 |
| 134 and 121 | 16214 |
| 188 and 56 | 2632 |
| 76 and 108 | 2052 |
| 39 and 148 | 5772 |