Least Common Multiple (LCM) of 133 and 123
The least common multiple (LCM) of 133 and 123 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 133 and 123?
First, calculate the GCD of 133 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 123 = 1 remainder 10 |
| 2 | 123 ÷ 10 = 12 remainder 3 |
| 3 | 10 ÷ 3 = 3 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 156 | 1092 |
| 189 and 135 | 945 |
| 13 and 180 | 2340 |
| 127 and 100 | 12700 |
| 161 and 117 | 18837 |