Least Common Multiple (LCM) of 80 and 119
The least common multiple (LCM) of 80 and 119 is 9520.
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 119?
First, calculate the GCD of 80 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 119 = 0 remainder 80 |
| 2 | 119 ÷ 80 = 1 remainder 39 |
| 3 | 80 ÷ 39 = 2 remainder 2 |
| 4 | 39 ÷ 2 = 19 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 60 | 960 |
| 118 and 55 | 6490 |
| 134 and 90 | 6030 |
| 25 and 120 | 600 |
| 89 and 10 | 890 |