Least Common Multiple (LCM) of 200 and 77
The least common multiple (LCM) of 200 and 77 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 77?
First, calculate the GCD of 200 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 77 = 2 remainder 46 |
| 2 | 77 ÷ 46 = 1 remainder 31 |
| 3 | 46 ÷ 31 = 1 remainder 15 |
| 4 | 31 ÷ 15 = 2 remainder 1 |
| 5 | 15 ÷ 1 = 15 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 66 | 3234 |
| 150 and 151 | 22650 |
| 77 and 137 | 10549 |
| 100 and 103 | 10300 |
| 55 and 103 | 5665 |