Least Common Multiple (LCM) of 108 and 67
The least common multiple (LCM) of 108 and 67 is 7236.
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 108 and 67?
First, calculate the GCD of 108 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 67 = 1 remainder 41 |
| 2 | 67 ÷ 41 = 1 remainder 26 |
| 3 | 41 ÷ 26 = 1 remainder 15 |
| 4 | 26 ÷ 15 = 1 remainder 11 |
| 5 | 15 ÷ 11 = 1 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 189 | 35532 |
| 41 and 71 | 2911 |
| 118 and 170 | 10030 |
| 149 and 178 | 26522 |
| 181 and 25 | 4525 |