Least Common Multiple (LCM) of 89 and 132
The least common multiple (LCM) of 89 and 132 is 11748.
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 132?
First, calculate the GCD of 89 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 132 = 0 remainder 89 |
| 2 | 132 ÷ 89 = 1 remainder 43 |
| 3 | 89 ÷ 43 = 2 remainder 3 |
| 4 | 43 ÷ 3 = 14 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 193 and 71 | 13703 |
| 149 and 159 | 23691 |
| 101 and 183 | 18483 |
| 117 and 175 | 20475 |
| 111 and 165 | 6105 |