Least Common Multiple (LCM) of 83 and 160
The least common multiple (LCM) of 83 and 160 is 13280.
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 83 and 160?
First, calculate the GCD of 83 and 160 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 160 = 0 remainder 83 |
| 2 | 160 ÷ 83 = 1 remainder 77 |
| 3 | 83 ÷ 77 = 1 remainder 6 |
| 4 | 77 ÷ 6 = 12 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 86 | 9890 |
| 46 and 102 | 2346 |
| 72 and 58 | 2088 |
| 163 and 178 | 29014 |
| 56 and 111 | 6216 |