Least Common Multiple (LCM) of 99 and 133
The least common multiple (LCM) of 99 and 133 is 13167.
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 99 and 133?
First, calculate the GCD of 99 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 99 ÷ 133 = 0 remainder 99 |
| 2 | 133 ÷ 99 = 1 remainder 34 |
| 3 | 99 ÷ 34 = 2 remainder 31 |
| 4 | 34 ÷ 31 = 1 remainder 3 |
| 5 | 31 ÷ 3 = 10 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 132 | 1188 |
| 129 and 33 | 1419 |
| 126 and 20 | 1260 |
| 101 and 68 | 6868 |
| 78 and 199 | 15522 |