Least Common Multiple (LCM) of 200 and 157
The least common multiple (LCM) of 200 and 157 is 31400.
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 157?
First, calculate the GCD of 200 and 157 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 157 = 1 remainder 43 |
| 2 | 157 ÷ 43 = 3 remainder 28 |
| 3 | 43 ÷ 28 = 1 remainder 15 |
| 4 | 28 ÷ 15 = 1 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 172 | 172 |
| 195 and 198 | 12870 |
| 172 and 148 | 6364 |
| 131 and 13 | 1703 |
| 75 and 32 | 2400 |