Least Common Multiple (LCM) of 110 and 65
The least common multiple (LCM) of 110 and 65 is 1430.
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 110 and 65?
First, calculate the GCD of 110 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 65 = 1 remainder 45 |
| 2 | 65 ÷ 45 = 1 remainder 20 |
| 3 | 45 ÷ 20 = 2 remainder 5 |
| 4 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 163 | 30481 |
| 164 and 90 | 7380 |
| 120 and 177 | 7080 |
| 186 and 121 | 22506 |
| 121 and 129 | 15609 |