Least Common Multiple (LCM) of 150 and 89
The least common multiple (LCM) of 150 and 89 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 150 and 89?
First, calculate the GCD of 150 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 89 = 1 remainder 61 |
| 2 | 89 ÷ 61 = 1 remainder 28 |
| 3 | 61 ÷ 28 = 2 remainder 5 |
| 4 | 28 ÷ 5 = 5 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 147 | 4263 |
| 62 and 105 | 6510 |
| 90 and 145 | 2610 |
| 200 and 164 | 8200 |
| 155 and 87 | 13485 |