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 |
|---|---|
| 147 and 148 | 21756 |
| 100 and 130 | 1300 |
| 24 and 173 | 4152 |
| 54 and 46 | 1242 |
| 96 and 59 | 5664 |