Least Common Multiple (LCM) of 114 and 89
The least common multiple (LCM) of 114 and 89 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 114 and 89?
First, calculate the GCD of 114 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 89 = 1 remainder 25 |
| 2 | 89 ÷ 25 = 3 remainder 14 |
| 3 | 25 ÷ 14 = 1 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 90 | 2610 |
| 84 and 92 | 1932 |
| 163 and 160 | 26080 |
| 134 and 120 | 8040 |
| 135 and 106 | 14310 |