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 |
|---|---|
| 172 and 111 | 19092 |
| 102 and 40 | 2040 |
| 36 and 10 | 180 |
| 148 and 84 | 3108 |
| 156 and 134 | 10452 |