Least Common Multiple (LCM) of 80 and 177
The least common multiple (LCM) of 80 and 177 is 14160.
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 177?
First, calculate the GCD of 80 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 177 = 0 remainder 80 |
| 2 | 177 ÷ 80 = 2 remainder 17 |
| 3 | 80 ÷ 17 = 4 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 108 | 13068 |
| 75 and 155 | 2325 |
| 37 and 192 | 7104 |
| 78 and 132 | 1716 |
| 150 and 44 | 3300 |