Least Common Multiple (LCM) of 91 and 137
The least common multiple (LCM) of 91 and 137 is 12467.
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 91 and 137?
First, calculate the GCD of 91 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 137 = 0 remainder 91 |
| 2 | 137 ÷ 91 = 1 remainder 46 |
| 3 | 91 ÷ 46 = 1 remainder 45 |
| 4 | 46 ÷ 45 = 1 remainder 1 |
| 5 | 45 ÷ 1 = 45 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 105 | 1785 |
| 192 and 72 | 576 |
| 21 and 169 | 3549 |
| 199 and 42 | 8358 |
| 193 and 30 | 5790 |