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 |
|---|---|
| 15 and 30 | 30 |
| 64 and 169 | 10816 |
| 168 and 145 | 24360 |
| 191 and 90 | 17190 |
| 169 and 112 | 18928 |