Least Common Multiple (LCM) of 110 and 123
The least common multiple (LCM) of 110 and 123 is 13530.
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 110 and 123?
First, calculate the GCD of 110 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 123 = 0 remainder 110 |
| 2 | 123 ÷ 110 = 1 remainder 13 |
| 3 | 110 ÷ 13 = 8 remainder 6 |
| 4 | 13 ÷ 6 = 2 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 36 | 252 |
| 62 and 185 | 11470 |
| 36 and 39 | 468 |
| 71 and 79 | 5609 |
| 49 and 106 | 5194 |