Least Common Multiple (LCM) of 83 and 165
The least common multiple (LCM) of 83 and 165 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 83 and 165?
First, calculate the GCD of 83 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 165 = 0 remainder 83 |
| 2 | 165 ÷ 83 = 1 remainder 82 |
| 3 | 83 ÷ 82 = 1 remainder 1 |
| 4 | 82 ÷ 1 = 82 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 74 | 7326 |
| 141 and 80 | 11280 |
| 114 and 99 | 3762 |
| 102 and 198 | 3366 |
| 169 and 116 | 19604 |