Least Common Multiple (LCM) of 133 and 85
The least common multiple (LCM) of 133 and 85 is 11305.
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 133 and 85?
First, calculate the GCD of 133 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 85 = 1 remainder 48 |
| 2 | 85 ÷ 48 = 1 remainder 37 |
| 3 | 48 ÷ 37 = 1 remainder 11 |
| 4 | 37 ÷ 11 = 3 remainder 4 |
| 5 | 11 ÷ 4 = 2 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 139 and 162 | 22518 |
| 14 and 186 | 1302 |
| 199 and 146 | 29054 |
| 164 and 143 | 23452 |
| 118 and 174 | 10266 |