Least Common Multiple (LCM) of 67 and 131
The least common multiple (LCM) of 67 and 131 is 8777.
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 131?
First, calculate the GCD of 67 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 131 = 0 remainder 67 |
| 2 | 131 ÷ 67 = 1 remainder 64 |
| 3 | 67 ÷ 64 = 1 remainder 3 |
| 4 | 64 ÷ 3 = 21 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 188 | 5640 |
| 127 and 182 | 23114 |
| 110 and 181 | 19910 |
| 173 and 187 | 32351 |
| 29 and 171 | 4959 |