Least Common Multiple (LCM) of 199 and 132
The least common multiple (LCM) of 199 and 132 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 199 and 132?
First, calculate the GCD of 199 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 132 = 1 remainder 67 |
| 2 | 132 ÷ 67 = 1 remainder 65 |
| 3 | 67 ÷ 65 = 1 remainder 2 |
| 4 | 65 ÷ 2 = 32 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 63 | 4095 |
| 77 and 88 | 616 |
| 137 and 149 | 20413 |
| 57 and 68 | 3876 |
| 104 and 162 | 8424 |