Least Common Multiple (LCM) of 83 and 144
The least common multiple (LCM) of 83 and 144 is 11952.
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 83 and 144?
First, calculate the GCD of 83 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 144 = 0 remainder 83 |
| 2 | 144 ÷ 83 = 1 remainder 61 |
| 3 | 83 ÷ 61 = 1 remainder 22 |
| 4 | 61 ÷ 22 = 2 remainder 17 |
| 5 | 22 ÷ 17 = 1 remainder 5 |
| 6 | 17 ÷ 5 = 3 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 12 | 420 |
| 111 and 166 | 18426 |
| 39 and 23 | 897 |
| 32 and 21 | 672 |
| 172 and 183 | 31476 |