Least Common Multiple (LCM) of 123 and 194
The least common multiple (LCM) of 123 and 194 is 23862.
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 194?
First, calculate the GCD of 123 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 194 = 0 remainder 123 |
| 2 | 194 ÷ 123 = 1 remainder 71 |
| 3 | 123 ÷ 71 = 1 remainder 52 |
| 4 | 71 ÷ 52 = 1 remainder 19 |
| 5 | 52 ÷ 19 = 2 remainder 14 |
| 6 | 19 ÷ 14 = 1 remainder 5 |
| 7 | 14 ÷ 5 = 2 remainder 4 |
| 8 | 5 ÷ 4 = 1 remainder 1 |
| 9 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 74 | 7770 |
| 192 and 195 | 12480 |
| 61 and 25 | 1525 |
| 196 and 154 | 2156 |
| 117 and 70 | 8190 |