Least Common Multiple (LCM) of 195 and 71
The least common multiple (LCM) of 195 and 71 is 13845.
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 71?
First, calculate the GCD of 195 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 71 = 2 remainder 53 |
| 2 | 71 ÷ 53 = 1 remainder 18 |
| 3 | 53 ÷ 18 = 2 remainder 17 |
| 4 | 18 ÷ 17 = 1 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 130 and 14 | 910 |
| 107 and 137 | 14659 |
| 69 and 96 | 2208 |
| 151 and 81 | 12231 |
| 56 and 134 | 3752 |