Least Common Multiple (LCM) of 109 and 20
The least common multiple (LCM) of 109 and 20 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 109 and 20?
First, calculate the GCD of 109 and 20 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 20 = 5 remainder 9 |
| 2 | 20 ÷ 9 = 2 remainder 2 |
| 3 | 9 ÷ 2 = 4 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 142 | 7810 |
| 83 and 137 | 11371 |
| 15 and 87 | 435 |
| 12 and 45 | 180 |
| 144 and 134 | 9648 |