Least Common Multiple (LCM) of 20 and 138
The least common multiple (LCM) of 20 and 138 is 1380.
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 138?
First, calculate the GCD of 20 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 138 = 0 remainder 20 |
| 2 | 138 ÷ 20 = 6 remainder 18 |
| 3 | 20 ÷ 18 = 1 remainder 2 |
| 4 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 77 | 2079 |
| 181 and 41 | 7421 |
| 104 and 37 | 3848 |
| 134 and 51 | 6834 |
| 194 and 40 | 3880 |