Least Common Multiple (LCM) of 83 and 196
The least common multiple (LCM) of 83 and 196 is 16268.
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 196?
First, calculate the GCD of 83 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 196 = 0 remainder 83 |
| 2 | 196 ÷ 83 = 2 remainder 30 |
| 3 | 83 ÷ 30 = 2 remainder 23 |
| 4 | 30 ÷ 23 = 1 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 89 | 5696 |
| 156 and 135 | 7020 |
| 72 and 162 | 648 |
| 138 and 177 | 8142 |
| 96 and 23 | 2208 |