Least Common Multiple (LCM) of 126 and 189
The least common multiple (LCM) of 126 and 189 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 126 and 189?
First, calculate the GCD of 126 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 189 = 0 remainder 126 |
| 2 | 189 ÷ 126 = 1 remainder 63 |
| 3 | 126 ÷ 63 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 164 | 2788 |
| 37 and 57 | 2109 |
| 136 and 160 | 2720 |
| 127 and 47 | 5969 |
| 124 and 17 | 2108 |