Least Common Multiple (LCM) of 138 and 80
The least common multiple (LCM) of 138 and 80 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 138 and 80?
First, calculate the GCD of 138 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 138 ÷ 80 = 1 remainder 58 |
| 2 | 80 ÷ 58 = 1 remainder 22 |
| 3 | 58 ÷ 22 = 2 remainder 14 |
| 4 | 22 ÷ 14 = 1 remainder 8 |
| 5 | 14 ÷ 8 = 1 remainder 6 |
| 6 | 8 ÷ 6 = 1 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 110 | 1100 |
| 193 and 162 | 31266 |
| 148 and 160 | 5920 |
| 198 and 126 | 1386 |
| 138 and 43 | 5934 |