Least Common Multiple (LCM) of 83 and 133
The least common multiple (LCM) of 83 and 133 is 11039.
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 133?
First, calculate the GCD of 83 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 133 = 0 remainder 83 |
| 2 | 133 ÷ 83 = 1 remainder 50 |
| 3 | 83 ÷ 50 = 1 remainder 33 |
| 4 | 50 ÷ 33 = 1 remainder 17 |
| 5 | 33 ÷ 17 = 1 remainder 16 |
| 6 | 17 ÷ 16 = 1 remainder 1 |
| 7 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 82 | 4182 |
| 195 and 103 | 20085 |
| 170 and 14 | 1190 |
| 64 and 196 | 3136 |
| 69 and 117 | 2691 |