Least Common Multiple (LCM) of 110 and 170
The least common multiple (LCM) of 110 and 170 is 1870.
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 170?
First, calculate the GCD of 110 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 170 = 0 remainder 110 |
| 2 | 170 ÷ 110 = 1 remainder 60 |
| 3 | 110 ÷ 60 = 1 remainder 50 |
| 4 | 60 ÷ 50 = 1 remainder 10 |
| 5 | 50 ÷ 10 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 105 | 1365 |
| 40 and 36 | 360 |
| 50 and 16 | 400 |
| 86 and 159 | 13674 |
| 134 and 61 | 8174 |