Least Common Multiple (LCM) of 80 and 101
The least common multiple (LCM) of 80 and 101 is 8080.
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 101?
First, calculate the GCD of 80 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 101 = 0 remainder 80 |
| 2 | 101 ÷ 80 = 1 remainder 21 |
| 3 | 80 ÷ 21 = 3 remainder 17 |
| 4 | 21 ÷ 17 = 1 remainder 4 |
| 5 | 17 ÷ 4 = 4 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 47 | 5499 |
| 105 and 59 | 6195 |
| 200 and 75 | 600 |
| 50 and 117 | 5850 |
| 36 and 105 | 1260 |