Least Common Multiple (LCM) of 114 and 189
The least common multiple (LCM) of 114 and 189 is 7182.
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 189?
First, calculate the GCD of 114 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 189 = 0 remainder 114 |
| 2 | 189 ÷ 114 = 1 remainder 75 |
| 3 | 114 ÷ 75 = 1 remainder 39 |
| 4 | 75 ÷ 39 = 1 remainder 36 |
| 5 | 39 ÷ 36 = 1 remainder 3 |
| 6 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 28 | 140 |
| 32 and 97 | 3104 |
| 78 and 98 | 3822 |
| 153 and 195 | 9945 |
| 11 and 162 | 1782 |