Least Common Multiple (LCM) of 132 and 195
The least common multiple (LCM) of 132 and 195 is 8580.
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 132 and 195?
First, calculate the GCD of 132 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 195 = 0 remainder 132 |
| 2 | 195 ÷ 132 = 1 remainder 63 |
| 3 | 132 ÷ 63 = 2 remainder 6 |
| 4 | 63 ÷ 6 = 10 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 42 | 2856 |
| 96 and 40 | 480 |
| 96 and 16 | 96 |
| 185 and 153 | 28305 |
| 158 and 172 | 13588 |