Least Common Multiple (LCM) of 183 and 67
The least common multiple (LCM) of 183 and 67 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 183 and 67?
First, calculate the GCD of 183 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 183 ÷ 67 = 2 remainder 49 |
| 2 | 67 ÷ 49 = 1 remainder 18 |
| 3 | 49 ÷ 18 = 2 remainder 13 |
| 4 | 18 ÷ 13 = 1 remainder 5 |
| 5 | 13 ÷ 5 = 2 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 186 | 3348 |
| 96 and 49 | 4704 |
| 13 and 35 | 455 |
| 187 and 131 | 24497 |
| 179 and 120 | 21480 |