Least Common Multiple (LCM) of 200 and 154
The least common multiple (LCM) of 200 and 154 is 15400.
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 154?
First, calculate the GCD of 200 and 154 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 154 = 1 remainder 46 |
| 2 | 154 ÷ 46 = 3 remainder 16 |
| 3 | 46 ÷ 16 = 2 remainder 14 |
| 4 | 16 ÷ 14 = 1 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 55 | 385 |
| 22 and 11 | 22 |
| 50 and 170 | 850 |
| 60 and 89 | 5340 |
| 60 and 54 | 540 |