Least Common Multiple (LCM) of 114 and 136
The least common multiple (LCM) of 114 and 136 is 7752.
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 136?
First, calculate the GCD of 114 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 136 = 0 remainder 114 |
| 2 | 136 ÷ 114 = 1 remainder 22 |
| 3 | 114 ÷ 22 = 5 remainder 4 |
| 4 | 22 ÷ 4 = 5 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 20 | 420 |
| 124 and 174 | 10788 |
| 182 and 172 | 15652 |
| 14 and 125 | 1750 |
| 198 and 197 | 39006 |