Least Common Multiple (LCM) of 89 and 150
The least common multiple (LCM) of 89 and 150 is 13350.
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 150?
First, calculate the GCD of 89 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 150 = 0 remainder 89 |
| 2 | 150 ÷ 89 = 1 remainder 61 |
| 3 | 89 ÷ 61 = 1 remainder 28 |
| 4 | 61 ÷ 28 = 2 remainder 5 |
| 5 | 28 ÷ 5 = 5 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 119 | 8925 |
| 113 and 83 | 9379 |
| 153 and 105 | 5355 |
| 170 and 182 | 15470 |
| 106 and 60 | 3180 |