Least Common Multiple (LCM) of 114 and 191
The least common multiple (LCM) of 114 and 191 is 21774.
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 114 and 191?
First, calculate the GCD of 114 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 191 = 0 remainder 114 |
| 2 | 191 ÷ 114 = 1 remainder 77 |
| 3 | 114 ÷ 77 = 1 remainder 37 |
| 4 | 77 ÷ 37 = 2 remainder 3 |
| 5 | 37 ÷ 3 = 12 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 15 | 570 |
| 39 and 100 | 3900 |
| 166 and 182 | 15106 |
| 53 and 66 | 3498 |
| 163 and 89 | 14507 |