Least Common Multiple (LCM) of 200 and 169
The least common multiple (LCM) of 200 and 169 is 33800.
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 169?
First, calculate the GCD of 200 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 169 = 1 remainder 31 |
| 2 | 169 ÷ 31 = 5 remainder 14 |
| 3 | 31 ÷ 14 = 2 remainder 3 |
| 4 | 14 ÷ 3 = 4 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 92 | 3772 |
| 14 and 157 | 2198 |
| 48 and 151 | 7248 |
| 131 and 199 | 26069 |
| 34 and 43 | 1462 |