Least Common Multiple (LCM) of 98 and 144
The least common multiple (LCM) of 98 and 144 is 7056.
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 144?
First, calculate the GCD of 98 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 144 = 0 remainder 98 |
| 2 | 144 ÷ 98 = 1 remainder 46 |
| 3 | 98 ÷ 46 = 2 remainder 6 |
| 4 | 46 ÷ 6 = 7 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 189 | 20790 |
| 144 and 185 | 26640 |
| 152 and 148 | 5624 |
| 174 and 114 | 3306 |
| 68 and 158 | 5372 |