Least Common Multiple (LCM) of 10 and 115
The least common multiple (LCM) of 10 and 115 is 230.
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 10 and 115?
First, calculate the GCD of 10 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 115 = 0 remainder 10 |
| 2 | 115 ÷ 10 = 11 remainder 5 |
| 3 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 150 | 1650 |
| 18 and 129 | 774 |
| 154 and 89 | 13706 |
| 193 and 190 | 36670 |
| 185 and 189 | 34965 |