Least Common Multiple (LCM) of 89 and 102
The least common multiple (LCM) of 89 and 102 is 9078.
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 89 and 102?
First, calculate the GCD of 89 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 102 = 0 remainder 89 |
| 2 | 102 ÷ 89 = 1 remainder 13 |
| 3 | 89 ÷ 13 = 6 remainder 11 |
| 4 | 13 ÷ 11 = 1 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 27 and 15 | 135 |
| 10 and 32 | 160 |
| 159 and 70 | 11130 |
| 185 and 45 | 1665 |
| 173 and 109 | 18857 |