Least Common Multiple (LCM) of 191 and 115
The least common multiple (LCM) of 191 and 115 is 21965.
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 115?
First, calculate the GCD of 191 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 115 = 1 remainder 76 |
| 2 | 115 ÷ 76 = 1 remainder 39 |
| 3 | 76 ÷ 39 = 1 remainder 37 |
| 4 | 39 ÷ 37 = 1 remainder 2 |
| 5 | 37 ÷ 2 = 18 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 53 | 1113 |
| 51 and 33 | 561 |
| 101 and 113 | 11413 |
| 93 and 158 | 14694 |
| 161 and 175 | 4025 |