Least Common Multiple (LCM) of 43 and 195
The least common multiple (LCM) of 43 and 195 is 8385.
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 43 and 195?
First, calculate the GCD of 43 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 195 = 0 remainder 43 |
| 2 | 195 ÷ 43 = 4 remainder 23 |
| 3 | 43 ÷ 23 = 1 remainder 20 |
| 4 | 23 ÷ 20 = 1 remainder 3 |
| 5 | 20 ÷ 3 = 6 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 46 and 45 | 2070 |
| 108 and 53 | 5724 |
| 148 and 52 | 1924 |
| 180 and 66 | 1980 |
| 34 and 143 | 4862 |