Least Common Multiple (LCM) of 106 and 133
The least common multiple (LCM) of 106 and 133 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 106 and 133?
First, calculate the GCD of 106 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 106 ÷ 133 = 0 remainder 106 |
| 2 | 133 ÷ 106 = 1 remainder 27 |
| 3 | 106 ÷ 27 = 3 remainder 25 |
| 4 | 27 ÷ 25 = 1 remainder 2 |
| 5 | 25 ÷ 2 = 12 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 86 | 1978 |
| 21 and 187 | 3927 |
| 112 and 168 | 336 |
| 105 and 163 | 17115 |
| 41 and 13 | 533 |