Least Common Multiple (LCM) of 114 and 11
The least common multiple (LCM) of 114 and 11 is 1254.
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 11?
First, calculate the GCD of 114 and 11 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 11 = 10 remainder 4 |
| 2 | 11 ÷ 4 = 2 remainder 3 |
| 3 | 4 ÷ 3 = 1 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 158 and 123 | 19434 |
| 174 and 11 | 1914 |
| 198 and 103 | 20394 |
| 113 and 190 | 21470 |
| 36 and 196 | 1764 |