Least Common Multiple (LCM) of 113 and 85
The least common multiple (LCM) of 113 and 85 is 9605.
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 113 and 85?
First, calculate the GCD of 113 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 85 = 1 remainder 28 |
| 2 | 85 ÷ 28 = 3 remainder 1 |
| 3 | 28 ÷ 1 = 28 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 37 | 1073 |
| 165 and 200 | 6600 |
| 199 and 105 | 20895 |
| 124 and 96 | 2976 |
| 102 and 188 | 9588 |