Least Common Multiple (LCM) of 89 and 170
The least common multiple (LCM) of 89 and 170 is 15130.
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 170?
First, calculate the GCD of 89 and 170 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 170 = 0 remainder 89 |
| 2 | 170 ÷ 89 = 1 remainder 81 |
| 3 | 89 ÷ 81 = 1 remainder 8 |
| 4 | 81 ÷ 8 = 10 remainder 1 |
| 5 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 53 | 9010 |
| 176 and 160 | 1760 |
| 61 and 113 | 6893 |
| 45 and 110 | 990 |
| 81 and 141 | 3807 |