Least Common Multiple (LCM) of 127 and 75
The least common multiple (LCM) of 127 and 75 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 127 and 75?
First, calculate the GCD of 127 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 75 = 1 remainder 52 |
| 2 | 75 ÷ 52 = 1 remainder 23 |
| 3 | 52 ÷ 23 = 2 remainder 6 |
| 4 | 23 ÷ 6 = 3 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 169 | 5070 |
| 37 and 27 | 999 |
| 58 and 14 | 406 |
| 54 and 90 | 270 |
| 121 and 122 | 14762 |