Least Common Multiple (LCM) of 126 and 76
The least common multiple (LCM) of 126 and 76 is 4788.
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 76?
First, calculate the GCD of 126 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 76 = 1 remainder 50 |
| 2 | 76 ÷ 50 = 1 remainder 26 |
| 3 | 50 ÷ 26 = 1 remainder 24 |
| 4 | 26 ÷ 24 = 1 remainder 2 |
| 5 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 49 | 1176 |
| 68 and 76 | 1292 |
| 198 and 24 | 792 |
| 13 and 81 | 1053 |
| 144 and 16 | 144 |