Least Common Multiple (LCM) of 118 and 91
The least common multiple (LCM) of 118 and 91 is 10738.
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 118 and 91?
First, calculate the GCD of 118 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 91 = 1 remainder 27 |
| 2 | 91 ÷ 27 = 3 remainder 10 |
| 3 | 27 ÷ 10 = 2 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 37 | 5772 |
| 144 and 31 | 4464 |
| 101 and 180 | 18180 |
| 115 and 112 | 12880 |
| 157 and 166 | 26062 |