Least Common Multiple (LCM) of 89 and 107
The least common multiple (LCM) of 89 and 107 is 9523.
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 107?
First, calculate the GCD of 89 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 107 = 0 remainder 89 |
| 2 | 107 ÷ 89 = 1 remainder 18 |
| 3 | 89 ÷ 18 = 4 remainder 17 |
| 4 | 18 ÷ 17 = 1 remainder 1 |
| 5 | 17 ÷ 1 = 17 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 84 | 4620 |
| 80 and 41 | 3280 |
| 29 and 128 | 3712 |
| 137 and 132 | 18084 |
| 117 and 95 | 11115 |