Least Common Multiple (LCM) of 195 and 123
The least common multiple (LCM) of 195 and 123 is 7995.
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 123?
First, calculate the GCD of 195 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 123 = 1 remainder 72 |
| 2 | 123 ÷ 72 = 1 remainder 51 |
| 3 | 72 ÷ 51 = 1 remainder 21 |
| 4 | 51 ÷ 21 = 2 remainder 9 |
| 5 | 21 ÷ 9 = 2 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 141 | 3666 |
| 24 and 47 | 1128 |
| 106 and 115 | 12190 |
| 109 and 54 | 5886 |
| 54 and 72 | 216 |