Least Common Multiple (LCM) of 90 and 193
The least common multiple (LCM) of 90 and 193 is 17370.
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 193?
First, calculate the GCD of 90 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 193 = 0 remainder 90 |
| 2 | 193 ÷ 90 = 2 remainder 13 |
| 3 | 90 ÷ 13 = 6 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 95 and 120 | 2280 |
| 105 and 58 | 6090 |
| 137 and 130 | 17810 |
| 103 and 116 | 11948 |
| 59 and 90 | 5310 |