Least Common Multiple (LCM) of 189 and 126
The least common multiple (LCM) of 189 and 126 is 378.
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 189 and 126?
First, calculate the GCD of 189 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 126 = 1 remainder 63 |
| 2 | 126 ÷ 63 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 175 | 30100 |
| 22 and 84 | 924 |
| 10 and 189 | 1890 |
| 93 and 195 | 6045 |
| 191 and 187 | 35717 |