Least Common Multiple (LCM) of 90 and 199
The least common multiple (LCM) of 90 and 199 is 17910.
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 90 and 199?
First, calculate the GCD of 90 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 199 = 0 remainder 90 |
| 2 | 199 ÷ 90 = 2 remainder 19 |
| 3 | 90 ÷ 19 = 4 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 50 | 650 |
| 52 and 101 | 5252 |
| 128 and 50 | 3200 |
| 119 and 45 | 5355 |
| 120 and 105 | 840 |