Least Common Multiple (LCM) of 133 and 195
The least common multiple (LCM) of 133 and 195 is 25935.
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 195?
First, calculate the GCD of 133 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 195 = 0 remainder 133 |
| 2 | 195 ÷ 133 = 1 remainder 62 |
| 3 | 133 ÷ 62 = 2 remainder 9 |
| 4 | 62 ÷ 9 = 6 remainder 8 |
| 5 | 9 ÷ 8 = 1 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 39 | 6708 |
| 188 and 117 | 21996 |
| 103 and 130 | 13390 |
| 146 and 94 | 6862 |
| 65 and 63 | 4095 |