Least Common Multiple (LCM) of 114 and 134
The least common multiple (LCM) of 114 and 134 is 7638.
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 134?
First, calculate the GCD of 114 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 134 = 0 remainder 114 |
| 2 | 134 ÷ 114 = 1 remainder 20 |
| 3 | 114 ÷ 20 = 5 remainder 14 |
| 4 | 20 ÷ 14 = 1 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 62 | 9238 |
| 51 and 66 | 1122 |
| 176 and 182 | 16016 |
| 37 and 112 | 4144 |
| 55 and 113 | 6215 |