Least Common Multiple (LCM) of 114 and 137
The least common multiple (LCM) of 114 and 137 is 15618.
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 137?
First, calculate the GCD of 114 and 137 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 137 = 0 remainder 114 |
| 2 | 137 ÷ 114 = 1 remainder 23 |
| 3 | 114 ÷ 23 = 4 remainder 22 |
| 4 | 23 ÷ 22 = 1 remainder 1 |
| 5 | 22 ÷ 1 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 164 | 3116 |
| 181 and 177 | 32037 |
| 113 and 182 | 20566 |
| 12 and 114 | 228 |
| 37 and 188 | 6956 |