Least Common Multiple (LCM) of 132 and 199
The least common multiple (LCM) of 132 and 199 is 26268.
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 199?
First, calculate the GCD of 132 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 199 = 0 remainder 132 |
| 2 | 199 ÷ 132 = 1 remainder 67 |
| 3 | 132 ÷ 67 = 1 remainder 65 |
| 4 | 67 ÷ 65 = 1 remainder 2 |
| 5 | 65 ÷ 2 = 32 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 68 | 340 |
| 44 and 144 | 1584 |
| 176 and 133 | 23408 |
| 80 and 51 | 4080 |
| 180 and 134 | 12060 |