Least Common Multiple (LCM) of 89 and 116
The least common multiple (LCM) of 89 and 116 is 10324.
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 116?
First, calculate the GCD of 89 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 116 = 0 remainder 89 |
| 2 | 116 ÷ 89 = 1 remainder 27 |
| 3 | 89 ÷ 27 = 3 remainder 8 |
| 4 | 27 ÷ 8 = 3 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 60 | 780 |
| 151 and 173 | 26123 |
| 115 and 127 | 14605 |
| 34 and 116 | 1972 |
| 76 and 146 | 5548 |