Least Common Multiple (LCM) of 126 and 195
The least common multiple (LCM) of 126 and 195 is 8190.
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 195?
First, calculate the GCD of 126 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 195 = 0 remainder 126 |
| 2 | 195 ÷ 126 = 1 remainder 69 |
| 3 | 126 ÷ 69 = 1 remainder 57 |
| 4 | 69 ÷ 57 = 1 remainder 12 |
| 5 | 57 ÷ 12 = 4 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 164 | 9348 |
| 120 and 108 | 1080 |
| 156 and 169 | 2028 |
| 108 and 108 | 108 |
| 63 and 128 | 8064 |