Least Common Multiple (LCM) of 113 and 109
The least common multiple (LCM) of 113 and 109 is 12317.
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 109?
First, calculate the GCD of 113 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 109 = 1 remainder 4 |
| 2 | 109 ÷ 4 = 27 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 31 | 31 |
| 112 and 90 | 5040 |
| 149 and 141 | 21009 |
| 90 and 170 | 1530 |
| 64 and 138 | 4416 |