Least Common Multiple (LCM) of 105 and 110
The least common multiple (LCM) of 105 and 110 is 2310.
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 110?
First, calculate the GCD of 105 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 110 = 0 remainder 105 |
| 2 | 110 ÷ 105 = 1 remainder 5 |
| 3 | 105 ÷ 5 = 21 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 25 | 775 |
| 41 and 105 | 4305 |
| 135 and 59 | 7965 |
| 164 and 130 | 10660 |
| 163 and 163 | 163 |