Least Common Multiple (LCM) of 114 and 121
The least common multiple (LCM) of 114 and 121 is 13794.
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 114 and 121?
First, calculate the GCD of 114 and 121 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 121 = 0 remainder 114 |
| 2 | 121 ÷ 114 = 1 remainder 7 |
| 3 | 114 ÷ 7 = 16 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 16 and 54 | 432 |
| 95 and 134 | 12730 |
| 142 and 166 | 11786 |
| 187 and 140 | 26180 |
| 197 and 70 | 13790 |