Least Common Multiple (LCM) of 126 and 187
The least common multiple (LCM) of 126 and 187 is 23562.
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 187?
First, calculate the GCD of 126 and 187 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 187 = 0 remainder 126 |
| 2 | 187 ÷ 126 = 1 remainder 61 |
| 3 | 126 ÷ 61 = 2 remainder 4 |
| 4 | 61 ÷ 4 = 15 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 10 and 189 | 1890 |
| 91 and 180 | 16380 |
| 30 and 113 | 3390 |
| 65 and 25 | 325 |
| 55 and 98 | 5390 |