Least Common Multiple (LCM) of 93 and 126
The least common multiple (LCM) of 93 and 126 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 93 and 126?
First, calculate the GCD of 93 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 93 ÷ 126 = 0 remainder 93 |
| 2 | 126 ÷ 93 = 1 remainder 33 |
| 3 | 93 ÷ 33 = 2 remainder 27 |
| 4 | 33 ÷ 27 = 1 remainder 6 |
| 5 | 27 ÷ 6 = 4 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 199 | 23482 |
| 36 and 54 | 108 |
| 131 and 138 | 18078 |
| 153 and 79 | 12087 |
| 55 and 10 | 110 |