Least Common Multiple (LCM) of 83 and 49
The least common multiple (LCM) of 83 and 49 is 4067.
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 49?
First, calculate the GCD of 83 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 49 = 1 remainder 34 |
| 2 | 49 ÷ 34 = 1 remainder 15 |
| 3 | 34 ÷ 15 = 2 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 99 | 17622 |
| 10 and 66 | 330 |
| 151 and 128 | 19328 |
| 114 and 55 | 6270 |
| 44 and 69 | 3036 |