Least Common Multiple (LCM) of 110 and 31
The least common multiple (LCM) of 110 and 31 is 3410.
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 31?
First, calculate the GCD of 110 and 31 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 31 = 3 remainder 17 |
| 2 | 31 ÷ 17 = 1 remainder 14 |
| 3 | 17 ÷ 14 = 1 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 117 | 1404 |
| 159 and 142 | 22578 |
| 195 and 62 | 12090 |
| 184 and 115 | 920 |
| 161 and 144 | 23184 |