Least Common Multiple (LCM) of 195 and 126
The least common multiple (LCM) of 195 and 126 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 195 and 126?
First, calculate the GCD of 195 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 126 = 1 remainder 69 |
| 2 | 126 ÷ 69 = 1 remainder 57 |
| 3 | 69 ÷ 57 = 1 remainder 12 |
| 4 | 57 ÷ 12 = 4 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 81 and 119 | 9639 |
| 146 and 51 | 7446 |
| 113 and 13 | 1469 |
| 124 and 102 | 6324 |
| 37 and 73 | 2701 |