Least Common Multiple (LCM) of 80 and 138
The least common multiple (LCM) of 80 and 138 is 5520.
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 80 and 138?
First, calculate the GCD of 80 and 138 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 138 = 0 remainder 80 |
| 2 | 138 ÷ 80 = 1 remainder 58 |
| 3 | 80 ÷ 58 = 1 remainder 22 |
| 4 | 58 ÷ 22 = 2 remainder 14 |
| 5 | 22 ÷ 14 = 1 remainder 8 |
| 6 | 14 ÷ 8 = 1 remainder 6 |
| 7 | 8 ÷ 6 = 1 remainder 2 |
| 8 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 41 and 149 | 6109 |
| 159 and 193 | 30687 |
| 125 and 184 | 23000 |
| 159 and 96 | 5088 |
| 34 and 189 | 6426 |