Least Common Multiple (LCM) of 127 and 135
The least common multiple (LCM) of 127 and 135 is 17145.
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 135?
First, calculate the GCD of 127 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 135 = 0 remainder 127 |
| 2 | 135 ÷ 127 = 1 remainder 8 |
| 3 | 127 ÷ 8 = 15 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 103 | 14420 |
| 85 and 38 | 3230 |
| 37 and 160 | 5920 |
| 90 and 97 | 8730 |
| 187 and 133 | 24871 |