Least Common Multiple (LCM) of 49 and 80
The least common multiple (LCM) of 49 and 80 is 3920.
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 49 and 80?
First, calculate the GCD of 49 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 80 = 0 remainder 49 |
| 2 | 80 ÷ 49 = 1 remainder 31 |
| 3 | 49 ÷ 31 = 1 remainder 18 |
| 4 | 31 ÷ 18 = 1 remainder 13 |
| 5 | 18 ÷ 13 = 1 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 29 | 5655 |
| 173 and 83 | 14359 |
| 23 and 100 | 2300 |
| 11 and 106 | 1166 |
| 105 and 39 | 1365 |