Least Common Multiple (LCM) of 116 and 127
The least common multiple (LCM) of 116 and 127 is 14732.
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 116 and 127?
First, calculate the GCD of 116 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 116 ÷ 127 = 0 remainder 116 |
| 2 | 127 ÷ 116 = 1 remainder 11 |
| 3 | 116 ÷ 11 = 10 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 |
|---|---|
| 51 and 20 | 1020 |
| 88 and 15 | 1320 |
| 81 and 31 | 2511 |
| 183 and 79 | 14457 |
| 37 and 175 | 6475 |