Least Common Multiple (LCM) of 75 and 126
The least common multiple (LCM) of 75 and 126 is 3150.
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 75 and 126?
First, calculate the GCD of 75 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 126 = 0 remainder 75 |
| 2 | 126 ÷ 75 = 1 remainder 51 |
| 3 | 75 ÷ 51 = 1 remainder 24 |
| 4 | 51 ÷ 24 = 2 remainder 3 |
| 5 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 117 | 1989 |
| 96 and 154 | 7392 |
| 76 and 199 | 15124 |
| 162 and 200 | 16200 |
| 43 and 82 | 3526 |