Least Common Multiple (LCM) of 59 and 191
The least common multiple (LCM) of 59 and 191 is 11269.
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 59 and 191?
First, calculate the GCD of 59 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 191 = 0 remainder 59 |
| 2 | 191 ÷ 59 = 3 remainder 14 |
| 3 | 59 ÷ 14 = 4 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 111 | 5106 |
| 199 and 19 | 3781 |
| 85 and 186 | 15810 |
| 179 and 63 | 11277 |
| 45 and 129 | 1935 |