Least Common Multiple (LCM) of 126 and 75
The least common multiple (LCM) of 126 and 75 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 126 and 75?
First, calculate the GCD of 126 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 75 = 1 remainder 51 |
| 2 | 75 ÷ 51 = 1 remainder 24 |
| 3 | 51 ÷ 24 = 2 remainder 3 |
| 4 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 29 | 5162 |
| 80 and 21 | 1680 |
| 178 and 106 | 9434 |
| 103 and 138 | 14214 |
| 16 and 123 | 1968 |