Least Common Multiple (LCM) of 200 and 170
The least common multiple (LCM) of 200 and 170 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 200 and 170?
First, calculate the GCD of 200 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 170 = 1 remainder 30 |
| 2 | 170 ÷ 30 = 5 remainder 20 |
| 3 | 30 ÷ 20 = 1 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 118 | 8850 |
| 161 and 120 | 19320 |
| 137 and 117 | 16029 |
| 105 and 129 | 4515 |
| 79 and 84 | 6636 |