Least Common Multiple (LCM) of 68 and 195
The least common multiple (LCM) of 68 and 195 is 13260.
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 68 and 195?
First, calculate the GCD of 68 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 195 = 0 remainder 68 |
| 2 | 195 ÷ 68 = 2 remainder 59 |
| 3 | 68 ÷ 59 = 1 remainder 9 |
| 4 | 59 ÷ 9 = 6 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 100 | 3600 |
| 40 and 175 | 1400 |
| 195 and 86 | 16770 |
| 68 and 142 | 4828 |
| 195 and 103 | 20085 |