Least Common Multiple (LCM) of 194 and 123
The least common multiple (LCM) of 194 and 123 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 194 and 123?
First, calculate the GCD of 194 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 123 = 1 remainder 71 |
| 2 | 123 ÷ 71 = 1 remainder 52 |
| 3 | 71 ÷ 52 = 1 remainder 19 |
| 4 | 52 ÷ 19 = 2 remainder 14 |
| 5 | 19 ÷ 14 = 1 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 11 | 1298 |
| 77 and 110 | 770 |
| 57 and 119 | 6783 |
| 14 and 180 | 1260 |
| 162 and 117 | 2106 |