Least Common Multiple (LCM) of 185 and 133
The least common multiple (LCM) of 185 and 133 is 24605.
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 185 and 133?
First, calculate the GCD of 185 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 133 = 1 remainder 52 |
| 2 | 133 ÷ 52 = 2 remainder 29 |
| 3 | 52 ÷ 29 = 1 remainder 23 |
| 4 | 29 ÷ 23 = 1 remainder 6 |
| 5 | 23 ÷ 6 = 3 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 101 | 18180 |
| 102 and 110 | 5610 |
| 36 and 113 | 4068 |
| 40 and 71 | 2840 |
| 149 and 85 | 12665 |