Least Common Multiple (LCM) of 67 and 183
The least common multiple (LCM) of 67 and 183 is 12261.
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 67 and 183?
First, calculate the GCD of 67 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 183 = 0 remainder 67 |
| 2 | 183 ÷ 67 = 2 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 |
|---|---|
| 172 and 199 | 34228 |
| 78 and 196 | 7644 |
| 85 and 113 | 9605 |
| 114 and 186 | 3534 |
| 151 and 44 | 6644 |