Least Common Multiple (LCM) of 67 and 181
The least common multiple (LCM) of 67 and 181 is 12127.
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 181?
First, calculate the GCD of 67 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 181 = 0 remainder 67 |
| 2 | 181 ÷ 67 = 2 remainder 47 |
| 3 | 67 ÷ 47 = 1 remainder 20 |
| 4 | 47 ÷ 20 = 2 remainder 7 |
| 5 | 20 ÷ 7 = 2 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 14 | 322 |
| 118 and 157 | 18526 |
| 103 and 53 | 5459 |
| 23 and 135 | 3105 |
| 27 and 167 | 4509 |