Least Common Multiple (LCM) of 115 and 18
The least common multiple (LCM) of 115 and 18 is 2070.
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 18?
First, calculate the GCD of 115 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 18 = 6 remainder 7 |
| 2 | 18 ÷ 7 = 2 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 144 | 9360 |
| 118 and 129 | 15222 |
| 18 and 80 | 720 |
| 181 and 78 | 14118 |
| 154 and 182 | 2002 |