Least Common Multiple (LCM) of 115 and 98
The least common multiple (LCM) of 115 and 98 is 11270.
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 115 and 98?
First, calculate the GCD of 115 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 98 = 1 remainder 17 |
| 2 | 98 ÷ 17 = 5 remainder 13 |
| 3 | 17 ÷ 13 = 1 remainder 4 |
| 4 | 13 ÷ 4 = 3 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 89 | 8900 |
| 70 and 57 | 3990 |
| 12 and 75 | 300 |
| 42 and 135 | 1890 |
| 34 and 29 | 986 |