Least Common Multiple (LCM) of 158 and 114
The least common multiple (LCM) of 158 and 114 is 9006.
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 158 and 114?
First, calculate the GCD of 158 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 158 ÷ 114 = 1 remainder 44 |
| 2 | 114 ÷ 44 = 2 remainder 26 |
| 3 | 44 ÷ 26 = 1 remainder 18 |
| 4 | 26 ÷ 18 = 1 remainder 8 |
| 5 | 18 ÷ 8 = 2 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 113 | 11865 |
| 158 and 200 | 15800 |
| 189 and 89 | 16821 |
| 89 and 149 | 13261 |
| 157 and 105 | 16485 |