Least Common Multiple (LCM) of 123 and 98
The least common multiple (LCM) of 123 and 98 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 123 and 98?
First, calculate the GCD of 123 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 98 = 1 remainder 25 |
| 2 | 98 ÷ 25 = 3 remainder 23 |
| 3 | 25 ÷ 23 = 1 remainder 2 |
| 4 | 23 ÷ 2 = 11 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 184 | 552 |
| 54 and 125 | 6750 |
| 163 and 80 | 13040 |
| 52 and 167 | 8684 |
| 129 and 142 | 18318 |