Least Common Multiple (LCM) of 80 and 188
The least common multiple (LCM) of 80 and 188 is 3760.
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 188?
First, calculate the GCD of 80 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 188 = 0 remainder 80 |
| 2 | 188 ÷ 80 = 2 remainder 28 |
| 3 | 80 ÷ 28 = 2 remainder 24 |
| 4 | 28 ÷ 24 = 1 remainder 4 |
| 5 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 180 | 8460 |
| 29 and 129 | 3741 |
| 142 and 27 | 3834 |
| 177 and 151 | 26727 |
| 79 and 108 | 8532 |