Least Common Multiple (LCM) of 109 and 183
The least common multiple (LCM) of 109 and 183 is 19947.
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 183?
First, calculate the GCD of 109 and 183 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 183 = 0 remainder 109 |
| 2 | 183 ÷ 109 = 1 remainder 74 |
| 3 | 109 ÷ 74 = 1 remainder 35 |
| 4 | 74 ÷ 35 = 2 remainder 4 |
| 5 | 35 ÷ 4 = 8 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 153 | 4896 |
| 72 and 167 | 12024 |
| 100 and 191 | 19100 |
| 114 and 144 | 2736 |
| 133 and 184 | 24472 |