Least Common Multiple (LCM) of 102 and 133
The least common multiple (LCM) of 102 and 133 is 13566.
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 102 and 133?
First, calculate the GCD of 102 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 133 = 0 remainder 102 |
| 2 | 133 ÷ 102 = 1 remainder 31 |
| 3 | 102 ÷ 31 = 3 remainder 9 |
| 4 | 31 ÷ 9 = 3 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 27 | 135 |
| 150 and 33 | 1650 |
| 40 and 107 | 4280 |
| 46 and 95 | 4370 |
| 75 and 33 | 825 |