Least Common Multiple (LCM) of 133 and 185
The least common multiple (LCM) of 133 and 185 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 133 and 185?
First, calculate the GCD of 133 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 185 = 0 remainder 133 |
| 2 | 185 ÷ 133 = 1 remainder 52 |
| 3 | 133 ÷ 52 = 2 remainder 29 |
| 4 | 52 ÷ 29 = 1 remainder 23 |
| 5 | 29 ÷ 23 = 1 remainder 6 |
| 6 | 23 ÷ 6 = 3 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 30 | 1020 |
| 123 and 34 | 4182 |
| 44 and 68 | 748 |
| 28 and 89 | 2492 |
| 34 and 61 | 2074 |