Least Common Multiple (LCM) of 137 and 191
The least common multiple (LCM) of 137 and 191 is 26167.
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 137 and 191?
First, calculate the GCD of 137 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 137 ÷ 191 = 0 remainder 137 |
| 2 | 191 ÷ 137 = 1 remainder 54 |
| 3 | 137 ÷ 54 = 2 remainder 29 |
| 4 | 54 ÷ 29 = 1 remainder 25 |
| 5 | 29 ÷ 25 = 1 remainder 4 |
| 6 | 25 ÷ 4 = 6 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 111 | 14874 |
| 66 and 67 | 4422 |
| 123 and 37 | 4551 |
| 78 and 134 | 5226 |
| 96 and 74 | 3552 |