Least Common Multiple (LCM) of 133 and 106
The least common multiple (LCM) of 133 and 106 is 14098.
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 106?
First, calculate the GCD of 133 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 106 = 1 remainder 27 |
| 2 | 106 ÷ 27 = 3 remainder 25 |
| 3 | 27 ÷ 25 = 1 remainder 2 |
| 4 | 25 ÷ 2 = 12 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 106 | 14522 |
| 195 and 83 | 16185 |
| 90 and 58 | 2610 |
| 155 and 44 | 6820 |
| 30 and 105 | 210 |