Least Common Multiple (LCM) of 183 and 116
The least common multiple (LCM) of 183 and 116 is 21228.
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 183 and 116?
First, calculate the GCD of 183 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 183 ÷ 116 = 1 remainder 67 |
| 2 | 116 ÷ 67 = 1 remainder 49 |
| 3 | 67 ÷ 49 = 1 remainder 18 |
| 4 | 49 ÷ 18 = 2 remainder 13 |
| 5 | 18 ÷ 13 = 1 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 131 | 10742 |
| 113 and 136 | 15368 |
| 107 and 185 | 19795 |
| 100 and 35 | 700 |
| 36 and 194 | 3492 |