Least Common Multiple (LCM) of 20 and 111
The least common multiple (LCM) of 20 and 111 is 2220.
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 111?
First, calculate the GCD of 20 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 111 = 0 remainder 20 |
| 2 | 111 ÷ 20 = 5 remainder 11 |
| 3 | 20 ÷ 11 = 1 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 166 | 10790 |
| 12 and 82 | 492 |
| 87 and 138 | 4002 |
| 137 and 123 | 16851 |
| 143 and 82 | 11726 |