Least Common Multiple (LCM) of 200 and 177
The least common multiple (LCM) of 200 and 177 is 35400.
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 177?
First, calculate the GCD of 200 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 177 = 1 remainder 23 |
| 2 | 177 ÷ 23 = 7 remainder 16 |
| 3 | 23 ÷ 16 = 1 remainder 7 |
| 4 | 16 ÷ 7 = 2 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 125 | 9000 |
| 15 and 154 | 2310 |
| 86 and 157 | 13502 |
| 24 and 31 | 744 |
| 130 and 170 | 2210 |