Least Common Multiple (LCM) of 200 and 19
The least common multiple (LCM) of 200 and 19 is 3800.
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 19?
First, calculate the GCD of 200 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 19 = 10 remainder 10 |
| 2 | 19 ÷ 10 = 1 remainder 9 |
| 3 | 10 ÷ 9 = 1 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 99 | 1980 |
| 172 and 161 | 27692 |
| 167 and 41 | 6847 |
| 114 and 85 | 9690 |
| 79 and 141 | 11139 |