Least Common Multiple (LCM) of 89 and 106
The least common multiple (LCM) of 89 and 106 is 9434.
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 106?
First, calculate the GCD of 89 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 106 = 0 remainder 89 |
| 2 | 106 ÷ 89 = 1 remainder 17 |
| 3 | 89 ÷ 17 = 5 remainder 4 |
| 4 | 17 ÷ 4 = 4 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 178 | 11392 |
| 171 and 104 | 17784 |
| 132 and 157 | 20724 |
| 116 and 72 | 2088 |
| 115 and 120 | 2760 |