Least Common Multiple (LCM) of 89 and 109
The least common multiple (LCM) of 89 and 109 is 9701.
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 109?
First, calculate the GCD of 89 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 109 = 0 remainder 89 |
| 2 | 109 ÷ 89 = 1 remainder 20 |
| 3 | 89 ÷ 20 = 4 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 176 and 95 | 16720 |
| 50 and 182 | 4550 |
| 154 and 176 | 1232 |
| 59 and 116 | 6844 |
| 19 and 56 | 1064 |