Least Common Multiple (LCM) of 123 and 195
The least common multiple (LCM) of 123 and 195 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 123 and 195?
First, calculate the GCD of 123 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 195 = 0 remainder 123 |
| 2 | 195 ÷ 123 = 1 remainder 72 |
| 3 | 123 ÷ 72 = 1 remainder 51 |
| 4 | 72 ÷ 51 = 1 remainder 21 |
| 5 | 51 ÷ 21 = 2 remainder 9 |
| 6 | 21 ÷ 9 = 2 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 170 | 1190 |
| 90 and 97 | 8730 |
| 124 and 182 | 11284 |
| 14 and 180 | 1260 |
| 120 and 140 | 840 |