Least Common Multiple (LCM) of 133 and 102
The least common multiple (LCM) of 133 and 102 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 133 and 102?
First, calculate the GCD of 133 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 102 = 1 remainder 31 |
| 2 | 102 ÷ 31 = 3 remainder 9 |
| 3 | 31 ÷ 9 = 3 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 111 | 4551 |
| 85 and 165 | 2805 |
| 60 and 50 | 300 |
| 117 and 193 | 22581 |
| 117 and 87 | 3393 |