Least Common Multiple (LCM) of 113 and 99
The least common multiple (LCM) of 113 and 99 is 11187.
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 99?
First, calculate the GCD of 113 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 99 = 1 remainder 14 |
| 2 | 99 ÷ 14 = 7 remainder 1 |
| 3 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 22 | 3454 |
| 39 and 39 | 39 |
| 177 and 70 | 12390 |
| 162 and 14 | 1134 |
| 165 and 29 | 4785 |