Least Common Multiple (LCM) of 110 and 171
The least common multiple (LCM) of 110 and 171 is 18810.
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 171?
First, calculate the GCD of 110 and 171 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 171 = 0 remainder 110 |
| 2 | 171 ÷ 110 = 1 remainder 61 |
| 3 | 110 ÷ 61 = 1 remainder 49 |
| 4 | 61 ÷ 49 = 1 remainder 12 |
| 5 | 49 ÷ 12 = 4 remainder 1 |
| 6 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 150 | 3150 |
| 187 and 30 | 5610 |
| 164 and 197 | 32308 |
| 162 and 41 | 6642 |
| 133 and 113 | 15029 |