Least Common Multiple (LCM) of 195 and 34
The least common multiple (LCM) of 195 and 34 is 6630.
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 34?
First, calculate the GCD of 195 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 34 = 5 remainder 25 |
| 2 | 34 ÷ 25 = 1 remainder 9 |
| 3 | 25 ÷ 9 = 2 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 77 | 14322 |
| 173 and 90 | 15570 |
| 132 and 194 | 12804 |
| 145 and 181 | 26245 |
| 158 and 140 | 11060 |