Least Common Multiple (LCM) of 83 and 170
The least common multiple (LCM) of 83 and 170 is 14110.
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 170?
First, calculate the GCD of 83 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 170 = 0 remainder 83 |
| 2 | 170 ÷ 83 = 2 remainder 4 |
| 3 | 83 ÷ 4 = 20 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 190 | 34770 |
| 165 and 167 | 27555 |
| 21 and 105 | 105 |
| 186 and 18 | 558 |
| 150 and 196 | 14700 |