Least Common Multiple (LCM) of 115 and 180
The least common multiple (LCM) of 115 and 180 is 4140.
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 180?
First, calculate the GCD of 115 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 180 = 0 remainder 115 |
| 2 | 180 ÷ 115 = 1 remainder 65 |
| 3 | 115 ÷ 65 = 1 remainder 50 |
| 4 | 65 ÷ 50 = 1 remainder 15 |
| 5 | 50 ÷ 15 = 3 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 53 | 8798 |
| 84 and 89 | 7476 |
| 96 and 57 | 1824 |
| 121 and 185 | 22385 |
| 101 and 28 | 2828 |