Least Common Multiple (LCM) of 90 and 150
The least common multiple (LCM) of 90 and 150 is 450.
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 90 and 150?
First, calculate the GCD of 90 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 150 = 0 remainder 90 |
| 2 | 150 ÷ 90 = 1 remainder 60 |
| 3 | 90 ÷ 60 = 1 remainder 30 |
| 4 | 60 ÷ 30 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 73 | 12483 |
| 107 and 82 | 8774 |
| 171 and 89 | 15219 |
| 17 and 165 | 2805 |
| 111 and 37 | 111 |