Least Common Multiple (LCM) of 75 and 127
The least common multiple (LCM) of 75 and 127 is 9525.
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 127?
First, calculate the GCD of 75 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 127 = 0 remainder 75 |
| 2 | 127 ÷ 75 = 1 remainder 52 |
| 3 | 75 ÷ 52 = 1 remainder 23 |
| 4 | 52 ÷ 23 = 2 remainder 6 |
| 5 | 23 ÷ 6 = 3 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 113 | 5650 |
| 113 and 84 | 9492 |
| 108 and 23 | 2484 |
| 196 and 200 | 9800 |
| 45 and 130 | 1170 |