Least Common Multiple (LCM) of 114 and 26
The least common multiple (LCM) of 114 and 26 is 1482.
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 26?
First, calculate the GCD of 114 and 26 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 26 = 4 remainder 10 |
| 2 | 26 ÷ 10 = 2 remainder 6 |
| 3 | 10 ÷ 6 = 1 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 55 | 2035 |
| 105 and 12 | 420 |
| 137 and 69 | 9453 |
| 168 and 127 | 21336 |
| 89 and 146 | 12994 |