Least Common Multiple (LCM) of 109 and 113
The least common multiple (LCM) of 109 and 113 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 109 and 113?
First, calculate the GCD of 109 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 113 = 0 remainder 109 |
| 2 | 113 ÷ 109 = 1 remainder 4 |
| 3 | 109 ÷ 4 = 27 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 144 and 158 | 11376 |
| 16 and 192 | 192 |
| 23 and 166 | 3818 |
| 179 and 98 | 17542 |
| 138 and 181 | 24978 |