Least Common Multiple (LCM) of 113 and 114
The least common multiple (LCM) of 113 and 114 is 12882.
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 113 and 114?
First, calculate the GCD of 113 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 114 = 0 remainder 113 |
| 2 | 114 ÷ 113 = 1 remainder 1 |
| 3 | 113 ÷ 1 = 113 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 142 | 11786 |
| 69 and 72 | 1656 |
| 106 and 192 | 10176 |
| 93 and 180 | 5580 |
| 30 and 34 | 510 |