Least Common Multiple (LCM) of 98 and 123
The least common multiple (LCM) of 98 and 123 is 12054.
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 98 and 123?
First, calculate the GCD of 98 and 123 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 123 = 0 remainder 98 |
| 2 | 123 ÷ 98 = 1 remainder 25 |
| 3 | 98 ÷ 25 = 3 remainder 23 |
| 4 | 25 ÷ 23 = 1 remainder 2 |
| 5 | 23 ÷ 2 = 11 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 19 | 475 |
| 178 and 71 | 12638 |
| 181 and 125 | 22625 |
| 155 and 107 | 16585 |
| 26 and 134 | 1742 |