Least Common Multiple (LCM) of 83 and 110
The least common multiple (LCM) of 83 and 110 is 9130.
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 110?
First, calculate the GCD of 83 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 110 = 0 remainder 83 |
| 2 | 110 ÷ 83 = 1 remainder 27 |
| 3 | 83 ÷ 27 = 3 remainder 2 |
| 4 | 27 ÷ 2 = 13 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 90 | 5310 |
| 47 and 85 | 3995 |
| 133 and 138 | 18354 |
| 106 and 53 | 106 |
| 196 and 56 | 392 |