Least Common Multiple (LCM) of 89 and 114
The least common multiple (LCM) of 89 and 114 is 10146.
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 89 and 114?
First, calculate the GCD of 89 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 114 = 0 remainder 89 |
| 2 | 114 ÷ 89 = 1 remainder 25 |
| 3 | 89 ÷ 25 = 3 remainder 14 |
| 4 | 25 ÷ 14 = 1 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 157 | 29359 |
| 187 and 58 | 10846 |
| 144 and 55 | 7920 |
| 49 and 154 | 1078 |
| 193 and 112 | 21616 |