Least Common Multiple (LCM) of 123 and 133
The least common multiple (LCM) of 123 and 133 is 16359.
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 123 and 133?
First, calculate the GCD of 123 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 133 = 0 remainder 123 |
| 2 | 133 ÷ 123 = 1 remainder 10 |
| 3 | 123 ÷ 10 = 12 remainder 3 |
| 4 | 10 ÷ 3 = 3 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 111 | 1110 |
| 99 and 88 | 792 |
| 163 and 14 | 2282 |
| 197 and 175 | 34475 |
| 105 and 67 | 7035 |