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 |
|---|---|
| 155 and 80 | 2480 |
| 176 and 95 | 16720 |
| 132 and 113 | 14916 |
| 130 and 87 | 11310 |
| 105 and 33 | 1155 |