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 |
|---|---|
| 118 and 130 | 7670 |
| 56 and 134 | 3752 |
| 85 and 53 | 4505 |
| 118 and 104 | 6136 |
| 85 and 66 | 5610 |