Least Common Multiple (LCM) of 150 and 90
The least common multiple (LCM) of 150 and 90 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 150 and 90?
First, calculate the GCD of 150 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 90 = 1 remainder 60 |
| 2 | 90 ÷ 60 = 1 remainder 30 |
| 3 | 60 ÷ 30 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 105 | 420 |
| 83 and 63 | 5229 |
| 32 and 20 | 160 |
| 158 and 159 | 25122 |
| 79 and 101 | 7979 |