Least Common Multiple (LCM) of 150 and 180
The least common multiple (LCM) of 150 and 180 is 900.
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 180?
First, calculate the GCD of 150 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 180 = 0 remainder 150 |
| 2 | 180 ÷ 150 = 1 remainder 30 |
| 3 | 150 ÷ 30 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 84 | 1344 |
| 151 and 37 | 5587 |
| 97 and 65 | 6305 |
| 144 and 67 | 9648 |
| 26 and 122 | 1586 |