Least Common Multiple (LCM) of 67 and 188
The least common multiple (LCM) of 67 and 188 is 12596.
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 188?
First, calculate the GCD of 67 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 188 = 0 remainder 67 |
| 2 | 188 ÷ 67 = 2 remainder 54 |
| 3 | 67 ÷ 54 = 1 remainder 13 |
| 4 | 54 ÷ 13 = 4 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 60 | 60 |
| 144 and 53 | 7632 |
| 84 and 124 | 2604 |
| 193 and 74 | 14282 |
| 128 and 82 | 5248 |