Least Common Multiple (LCM) of 127 and 138
The least common multiple (LCM) of 127 and 138 is 17526.
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 138?
First, calculate the GCD of 127 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 138 = 0 remainder 127 |
| 2 | 138 ÷ 127 = 1 remainder 11 |
| 3 | 127 ÷ 11 = 11 remainder 6 |
| 4 | 11 ÷ 6 = 1 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 120 | 360 |
| 60 and 110 | 660 |
| 189 and 165 | 10395 |
| 52 and 168 | 2184 |
| 32 and 139 | 4448 |