Least Common Multiple (LCM) of 103 and 89
The least common multiple (LCM) of 103 and 89 is 9167.
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 103 and 89?
First, calculate the GCD of 103 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 89 = 1 remainder 14 |
| 2 | 89 ÷ 14 = 6 remainder 5 |
| 3 | 14 ÷ 5 = 2 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 151 | 15251 |
| 186 and 148 | 13764 |
| 40 and 51 | 2040 |
| 110 and 45 | 990 |
| 35 and 158 | 5530 |