Least Common Multiple (LCM) of 105 and 115
The least common multiple (LCM) of 105 and 115 is 2415.
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 105 and 115?
First, calculate the GCD of 105 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 115 = 0 remainder 105 |
| 2 | 115 ÷ 105 = 1 remainder 10 |
| 3 | 105 ÷ 10 = 10 remainder 5 |
| 4 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 85 | 1360 |
| 186 and 175 | 32550 |
| 173 and 75 | 12975 |
| 43 and 168 | 7224 |
| 36 and 66 | 396 |