Least Common Multiple (LCM) of 83 and 169
The least common multiple (LCM) of 83 and 169 is 14027.
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 169?
First, calculate the GCD of 83 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 169 = 0 remainder 83 |
| 2 | 169 ÷ 83 = 2 remainder 3 |
| 3 | 83 ÷ 3 = 27 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 107 | 5671 |
| 50 and 41 | 2050 |
| 98 and 37 | 3626 |
| 54 and 54 | 54 |
| 110 and 100 | 1100 |