Least Common Multiple (LCM) of 113 and 91
The least common multiple (LCM) of 113 and 91 is 10283.
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 113 and 91?
First, calculate the GCD of 113 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 91 = 1 remainder 22 |
| 2 | 91 ÷ 22 = 4 remainder 3 |
| 3 | 22 ÷ 3 = 7 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 127 | 9525 |
| 13 and 105 | 1365 |
| 53 and 158 | 8374 |
| 120 and 120 | 120 |
| 109 and 22 | 2398 |