Least Common Multiple (LCM) of 115 and 40
The least common multiple (LCM) of 115 and 40 is 920.
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 115 and 40?
First, calculate the GCD of 115 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 40 = 2 remainder 35 |
| 2 | 40 ÷ 35 = 1 remainder 5 |
| 3 | 35 ÷ 5 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 82 | 164 |
| 45 and 120 | 360 |
| 148 and 172 | 6364 |
| 108 and 19 | 2052 |
| 129 and 162 | 6966 |