Least Common Multiple (LCM) of 195 and 38
The least common multiple (LCM) of 195 and 38 is 7410.
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 195 and 38?
First, calculate the GCD of 195 and 38 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 38 = 5 remainder 5 |
| 2 | 38 ÷ 5 = 7 remainder 3 |
| 3 | 5 ÷ 3 = 1 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 185 | 5735 |
| 129 and 85 | 10965 |
| 13 and 141 | 1833 |
| 43 and 147 | 6321 |
| 53 and 182 | 9646 |