Least Common Multiple (LCM) of 145 and 90
The least common multiple (LCM) of 145 and 90 is 2610.
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 145 and 90?
First, calculate the GCD of 145 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 90 = 1 remainder 55 |
| 2 | 90 ÷ 55 = 1 remainder 35 |
| 3 | 55 ÷ 35 = 1 remainder 20 |
| 4 | 35 ÷ 20 = 1 remainder 15 |
| 5 | 20 ÷ 15 = 1 remainder 5 |
| 6 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 83 | 11786 |
| 135 and 159 | 7155 |
| 85 and 33 | 2805 |
| 141 and 130 | 18330 |
| 54 and 81 | 162 |