Least Common Multiple (LCM) of 114 and 154
The least common multiple (LCM) of 114 and 154 is 8778.
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 154?
First, calculate the GCD of 114 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 154 = 0 remainder 114 |
| 2 | 154 ÷ 114 = 1 remainder 40 |
| 3 | 114 ÷ 40 = 2 remainder 34 |
| 4 | 40 ÷ 34 = 1 remainder 6 |
| 5 | 34 ÷ 6 = 5 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 199 | 32039 |
| 60 and 22 | 660 |
| 197 and 37 | 7289 |
| 122 and 52 | 3172 |
| 168 and 36 | 504 |