Least Common Multiple (LCM) of 127 and 140
The least common multiple (LCM) of 127 and 140 is 17780.
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 140?
First, calculate the GCD of 127 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 140 = 0 remainder 127 |
| 2 | 140 ÷ 127 = 1 remainder 13 |
| 3 | 127 ÷ 13 = 9 remainder 10 |
| 4 | 13 ÷ 10 = 1 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 138 | 14214 |
| 72 and 20 | 360 |
| 63 and 63 | 63 |
| 197 and 25 | 4925 |
| 191 and 48 | 9168 |