Least Common Multiple (LCM) of 67 and 108
The least common multiple (LCM) of 67 and 108 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 67 and 108?
First, calculate the GCD of 67 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 108 = 0 remainder 67 |
| 2 | 108 ÷ 67 = 1 remainder 41 |
| 3 | 67 ÷ 41 = 1 remainder 26 |
| 4 | 41 ÷ 26 = 1 remainder 15 |
| 5 | 26 ÷ 15 = 1 remainder 11 |
| 6 | 15 ÷ 11 = 1 remainder 4 |
| 7 | 11 ÷ 4 = 2 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 79 | 12640 |
| 171 and 197 | 33687 |
| 175 and 149 | 26075 |
| 156 and 80 | 3120 |
| 95 and 54 | 5130 |