Least Common Multiple (LCM) of 195 and 141
The least common multiple (LCM) of 195 and 141 is 9165.
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 141?
First, calculate the GCD of 195 and 141 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 141 = 1 remainder 54 |
| 2 | 141 ÷ 54 = 2 remainder 33 |
| 3 | 54 ÷ 33 = 1 remainder 21 |
| 4 | 33 ÷ 21 = 1 remainder 12 |
| 5 | 21 ÷ 12 = 1 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 93 | 15252 |
| 123 and 11 | 1353 |
| 80 and 56 | 560 |
| 130 and 39 | 390 |
| 27 and 79 | 2133 |