Least Common Multiple (LCM) of 83 and 179
The least common multiple (LCM) of 83 and 179 is 14857.
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 179?
First, calculate the GCD of 83 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 179 = 0 remainder 83 |
| 2 | 179 ÷ 83 = 2 remainder 13 |
| 3 | 83 ÷ 13 = 6 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 116 | 5684 |
| 128 and 119 | 15232 |
| 182 and 154 | 2002 |
| 21 and 178 | 3738 |
| 39 and 200 | 7800 |