Least Common Multiple (LCM) of 67 and 133
The least common multiple (LCM) of 67 and 133 is 8911.
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 133?
First, calculate the GCD of 67 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 133 = 0 remainder 67 |
| 2 | 133 ÷ 67 = 1 remainder 66 |
| 3 | 67 ÷ 66 = 1 remainder 1 |
| 4 | 66 ÷ 1 = 66 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 100 | 8300 |
| 92 and 167 | 15364 |
| 130 and 12 | 780 |
| 20 and 109 | 2180 |
| 139 and 133 | 18487 |