Least Common Multiple (LCM) of 191 and 114
The least common multiple (LCM) of 191 and 114 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 191 and 114?
First, calculate the GCD of 191 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 114 = 1 remainder 77 |
| 2 | 114 ÷ 77 = 1 remainder 37 |
| 3 | 77 ÷ 37 = 2 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 155 | 5735 |
| 62 and 136 | 4216 |
| 112 and 194 | 10864 |
| 105 and 169 | 17745 |
| 106 and 144 | 7632 |