Least Common Multiple (LCM) of 165 and 83
The least common multiple (LCM) of 165 and 83 is 13695.
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 165 and 83?
First, calculate the GCD of 165 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 165 ÷ 83 = 1 remainder 82 |
| 2 | 83 ÷ 82 = 1 remainder 1 |
| 3 | 82 ÷ 1 = 82 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 20 | 820 |
| 129 and 110 | 14190 |
| 161 and 141 | 22701 |
| 25 and 163 | 4075 |
| 104 and 158 | 8216 |