Least Common Multiple (LCM) of 177 and 200
The least common multiple (LCM) of 177 and 200 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 177 and 200?
First, calculate the GCD of 177 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 200 = 0 remainder 177 |
| 2 | 200 ÷ 177 = 1 remainder 23 |
| 3 | 177 ÷ 23 = 7 remainder 16 |
| 4 | 23 ÷ 16 = 1 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 188 and 165 | 31020 |
| 154 and 96 | 7392 |
| 42 and 150 | 1050 |
| 123 and 46 | 5658 |
| 136 and 181 | 24616 |