Least Common Multiple (LCM) of 76 and 115
The least common multiple (LCM) of 76 and 115 is 8740.
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 76 and 115?
First, calculate the GCD of 76 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 76 ÷ 115 = 0 remainder 76 |
| 2 | 115 ÷ 76 = 1 remainder 39 |
| 3 | 76 ÷ 39 = 1 remainder 37 |
| 4 | 39 ÷ 37 = 1 remainder 2 |
| 5 | 37 ÷ 2 = 18 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 14 | 826 |
| 146 and 165 | 24090 |
| 157 and 41 | 6437 |
| 147 and 90 | 4410 |
| 92 and 190 | 8740 |