Least Common Multiple (LCM) of 109 and 98
The least common multiple (LCM) of 109 and 98 is 10682.
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 109 and 98?
First, calculate the GCD of 109 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 98 = 1 remainder 11 |
| 2 | 98 ÷ 11 = 8 remainder 10 |
| 3 | 11 ÷ 10 = 1 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 50 and 120 | 600 |
| 162 and 152 | 12312 |
| 101 and 193 | 19493 |
| 197 and 81 | 15957 |
| 159 and 86 | 13674 |