Least Common Multiple (LCM) of 80 and 116
The least common multiple (LCM) of 80 and 116 is 2320.
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 116?
First, calculate the GCD of 80 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 116 = 0 remainder 80 |
| 2 | 116 ÷ 80 = 1 remainder 36 |
| 3 | 80 ÷ 36 = 2 remainder 8 |
| 4 | 36 ÷ 8 = 4 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 45 | 1710 |
| 46 and 173 | 7958 |
| 173 and 78 | 13494 |
| 143 and 65 | 715 |
| 189 and 150 | 9450 |