Least Common Multiple (LCM) of 163 and 83
The least common multiple (LCM) of 163 and 83 is 13529.
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 163 and 83?
First, calculate the GCD of 163 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 163 ÷ 83 = 1 remainder 80 |
| 2 | 83 ÷ 80 = 1 remainder 3 |
| 3 | 80 ÷ 3 = 26 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 71 | 852 |
| 145 and 73 | 10585 |
| 101 and 156 | 15756 |
| 105 and 10 | 210 |
| 76 and 54 | 2052 |