Least Common Multiple (LCM) of 190 and 123
The least common multiple (LCM) of 190 and 123 is 23370.
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 190 and 123?
First, calculate the GCD of 190 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 190 ÷ 123 = 1 remainder 67 |
| 2 | 123 ÷ 67 = 1 remainder 56 |
| 3 | 67 ÷ 56 = 1 remainder 11 |
| 4 | 56 ÷ 11 = 5 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 57 | 3078 |
| 46 and 98 | 2254 |
| 69 and 180 | 4140 |
| 90 and 146 | 6570 |
| 163 and 143 | 23309 |