Least Common Multiple (LCM) of 126 and 93
The least common multiple (LCM) of 126 and 93 is 3906.
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 93?
First, calculate the GCD of 126 and 93 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 93 = 1 remainder 33 |
| 2 | 93 ÷ 33 = 2 remainder 27 |
| 3 | 33 ÷ 27 = 1 remainder 6 |
| 4 | 27 ÷ 6 = 4 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 123 | 3813 |
| 83 and 100 | 8300 |
| 120 and 64 | 960 |
| 125 and 84 | 10500 |
| 65 and 158 | 10270 |