Least Common Multiple (LCM) of 67 and 182
The least common multiple (LCM) of 67 and 182 is 12194.
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 182?
First, calculate the GCD of 67 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 182 = 0 remainder 67 |
| 2 | 182 ÷ 67 = 2 remainder 48 |
| 3 | 67 ÷ 48 = 1 remainder 19 |
| 4 | 48 ÷ 19 = 2 remainder 10 |
| 5 | 19 ÷ 10 = 1 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 158 | 12640 |
| 110 and 120 | 1320 |
| 137 and 146 | 20002 |
| 67 and 24 | 1608 |
| 186 and 83 | 15438 |