Least Common Multiple (LCM) of 98 and 113
The least common multiple (LCM) of 98 and 113 is 11074.
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 113?
First, calculate the GCD of 98 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 113 = 0 remainder 98 |
| 2 | 113 ÷ 98 = 1 remainder 15 |
| 3 | 98 ÷ 15 = 6 remainder 8 |
| 4 | 15 ÷ 8 = 1 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 105 | 6510 |
| 157 and 90 | 14130 |
| 138 and 129 | 5934 |
| 127 and 103 | 13081 |
| 41 and 29 | 1189 |