Least Common Multiple (LCM) of 105 and 89
The least common multiple (LCM) of 105 and 89 is 9345.
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 105 and 89?
First, calculate the GCD of 105 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 89 = 1 remainder 16 |
| 2 | 89 ÷ 16 = 5 remainder 9 |
| 3 | 16 ÷ 9 = 1 remainder 7 |
| 4 | 9 ÷ 7 = 1 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 81 | 4293 |
| 112 and 143 | 16016 |
| 19 and 196 | 3724 |
| 103 and 138 | 14214 |
| 93 and 164 | 15252 |