Least Common Multiple (LCM) of 83 and 17
The least common multiple (LCM) of 83 and 17 is 1411.
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 17?
First, calculate the GCD of 83 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 17 = 4 remainder 15 |
| 2 | 17 ÷ 15 = 1 remainder 2 |
| 3 | 15 ÷ 2 = 7 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 53 | 5724 |
| 115 and 113 | 12995 |
| 33 and 114 | 1254 |
| 32 and 110 | 1760 |
| 34 and 84 | 1428 |