Least Common Multiple (LCM) of 159 and 200
The least common multiple (LCM) of 159 and 200 is 31800.
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 159 and 200?
First, calculate the GCD of 159 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 159 ÷ 200 = 0 remainder 159 |
| 2 | 200 ÷ 159 = 1 remainder 41 |
| 3 | 159 ÷ 41 = 3 remainder 36 |
| 4 | 41 ÷ 36 = 1 remainder 5 |
| 5 | 36 ÷ 5 = 7 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 172 | 32508 |
| 163 and 196 | 31948 |
| 14 and 109 | 1526 |
| 58 and 125 | 7250 |
| 22 and 154 | 154 |