Least Common Multiple (LCM) of 116 and 137
The least common multiple (LCM) of 116 and 137 is 15892.
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 116 and 137?
First, calculate the GCD of 116 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 137 = 0 remainder 116 |
| 2 | 137 ÷ 116 = 1 remainder 21 |
| 3 | 116 ÷ 21 = 5 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 64 | 320 |
| 165 and 185 | 6105 |
| 15 and 188 | 2820 |
| 119 and 46 | 5474 |
| 27 and 125 | 3375 |