Least Common Multiple (LCM) of 42 and 195
The least common multiple (LCM) of 42 and 195 is 2730.
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 42 and 195?
First, calculate the GCD of 42 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 195 = 0 remainder 42 |
| 2 | 195 ÷ 42 = 4 remainder 27 |
| 3 | 42 ÷ 27 = 1 remainder 15 |
| 4 | 27 ÷ 15 = 1 remainder 12 |
| 5 | 15 ÷ 12 = 1 remainder 3 |
| 6 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 195 and 169 | 2535 |
| 185 and 125 | 4625 |
| 21 and 165 | 1155 |
| 15 and 114 | 570 |
| 144 and 113 | 16272 |