Least Common Multiple (LCM) of 170 and 200
The least common multiple (LCM) of 170 and 200 is 3400.
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 170 and 200?
First, calculate the GCD of 170 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 170 ÷ 200 = 0 remainder 170 |
| 2 | 200 ÷ 170 = 1 remainder 30 |
| 3 | 170 ÷ 30 = 5 remainder 20 |
| 4 | 30 ÷ 20 = 1 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 130 | 1040 |
| 65 and 141 | 9165 |
| 134 and 149 | 19966 |
| 193 and 124 | 23932 |
| 65 and 119 | 7735 |