Least Common Multiple (LCM) of 80 and 133
The least common multiple (LCM) of 80 and 133 is 10640.
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 133?
First, calculate the GCD of 80 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 133 = 0 remainder 80 |
| 2 | 133 ÷ 80 = 1 remainder 53 |
| 3 | 80 ÷ 53 = 1 remainder 27 |
| 4 | 53 ÷ 27 = 1 remainder 26 |
| 5 | 27 ÷ 26 = 1 remainder 1 |
| 6 | 26 ÷ 1 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 65 | 7020 |
| 113 and 16 | 1808 |
| 79 and 134 | 10586 |
| 106 and 178 | 9434 |
| 81 and 186 | 5022 |