Least Common Multiple (LCM) of 200 and 123
The least common multiple (LCM) of 200 and 123 is 24600.
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 200 and 123?
First, calculate the GCD of 200 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 123 = 1 remainder 77 |
| 2 | 123 ÷ 77 = 1 remainder 46 |
| 3 | 77 ÷ 46 = 1 remainder 31 |
| 4 | 46 ÷ 31 = 1 remainder 15 |
| 5 | 31 ÷ 15 = 2 remainder 1 |
| 6 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 104 | 2184 |
| 49 and 79 | 3871 |
| 121 and 77 | 847 |
| 61 and 181 | 11041 |
| 30 and 118 | 1770 |