Least Common Multiple (LCM) of 102 and 115
The least common multiple (LCM) of 102 and 115 is 11730.
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 102 and 115?
First, calculate the GCD of 102 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 115 = 0 remainder 102 |
| 2 | 115 ÷ 102 = 1 remainder 13 |
| 3 | 102 ÷ 13 = 7 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 19 | 1235 |
| 148 and 102 | 7548 |
| 165 and 146 | 24090 |
| 76 and 95 | 380 |
| 129 and 13 | 1677 |