Least Common Multiple (LCM) of 195 and 42
The least common multiple (LCM) of 195 and 42 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 195 and 42?
First, calculate the GCD of 195 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 42 = 4 remainder 27 |
| 2 | 42 ÷ 27 = 1 remainder 15 |
| 3 | 27 ÷ 15 = 1 remainder 12 |
| 4 | 15 ÷ 12 = 1 remainder 3 |
| 5 | 12 ÷ 3 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 29 | 580 |
| 64 and 60 | 960 |
| 45 and 39 | 585 |
| 25 and 111 | 2775 |
| 160 and 200 | 800 |