Least Common Multiple (LCM) of 83 and 185
The least common multiple (LCM) of 83 and 185 is 15355.
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 185?
First, calculate the GCD of 83 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 185 = 0 remainder 83 |
| 2 | 185 ÷ 83 = 2 remainder 19 |
| 3 | 83 ÷ 19 = 4 remainder 7 |
| 4 | 19 ÷ 7 = 2 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 53 | 1749 |
| 156 and 101 | 15756 |
| 196 and 160 | 7840 |
| 101 and 20 | 2020 |
| 97 and 134 | 12998 |