Least Common Multiple (LCM) of 91 and 116
The least common multiple (LCM) of 91 and 116 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 91 and 116?
First, calculate the GCD of 91 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 116 = 0 remainder 91 |
| 2 | 116 ÷ 91 = 1 remainder 25 |
| 3 | 91 ÷ 25 = 3 remainder 16 |
| 4 | 25 ÷ 16 = 1 remainder 9 |
| 5 | 16 ÷ 9 = 1 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 31 | 1054 |
| 149 and 174 | 25926 |
| 44 and 65 | 2860 |
| 199 and 14 | 2786 |
| 133 and 31 | 4123 |