Least Common Multiple (LCM) of 103 and 133
The least common multiple (LCM) of 103 and 133 is 13699.
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 103 and 133?
First, calculate the GCD of 103 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 133 = 0 remainder 103 |
| 2 | 133 ÷ 103 = 1 remainder 30 |
| 3 | 103 ÷ 30 = 3 remainder 13 |
| 4 | 30 ÷ 13 = 2 remainder 4 |
| 5 | 13 ÷ 4 = 3 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 137 | 22605 |
| 173 and 198 | 34254 |
| 150 and 79 | 11850 |
| 184 and 140 | 6440 |
| 142 and 63 | 8946 |