Least Common Multiple (LCM) of 116 and 91
The least common multiple (LCM) of 116 and 91 is 10556.
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 91?
First, calculate the GCD of 116 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 91 = 1 remainder 25 |
| 2 | 91 ÷ 25 = 3 remainder 16 |
| 3 | 25 ÷ 16 = 1 remainder 9 |
| 4 | 16 ÷ 9 = 1 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 197 | 35460 |
| 79 and 168 | 13272 |
| 188 and 31 | 5828 |
| 102 and 156 | 2652 |
| 134 and 115 | 15410 |