Least Common Multiple (LCM) of 89 and 195
The least common multiple (LCM) of 89 and 195 is 17355.
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 89 and 195?
First, calculate the GCD of 89 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 195 = 0 remainder 89 |
| 2 | 195 ÷ 89 = 2 remainder 17 |
| 3 | 89 ÷ 17 = 5 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 110 | 990 |
| 30 and 53 | 1590 |
| 85 and 21 | 1785 |
| 103 and 169 | 17407 |
| 68 and 179 | 12172 |