Least Common Multiple (LCM) of 133 and 99
The least common multiple (LCM) of 133 and 99 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 133 and 99?
First, calculate the GCD of 133 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 99 = 1 remainder 34 |
| 2 | 99 ÷ 34 = 2 remainder 31 |
| 3 | 34 ÷ 31 = 1 remainder 3 |
| 4 | 31 ÷ 3 = 10 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 185 | 19980 |
| 191 and 39 | 7449 |
| 112 and 120 | 1680 |
| 100 and 15 | 300 |
| 78 and 177 | 4602 |