Least Common Multiple (LCM) of 20 and 109
The least common multiple (LCM) of 20 and 109 is 2180.
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 20 and 109?
First, calculate the GCD of 20 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 109 = 0 remainder 20 |
| 2 | 109 ÷ 20 = 5 remainder 9 |
| 3 | 20 ÷ 9 = 2 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 109 | 2616 |
| 160 and 35 | 1120 |
| 23 and 169 | 3887 |
| 161 and 184 | 1288 |
| 181 and 17 | 3077 |