Least Common Multiple (LCM) of 90 and 145
The least common multiple (LCM) of 90 and 145 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 90 and 145?
First, calculate the GCD of 90 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 145 = 0 remainder 90 |
| 2 | 145 ÷ 90 = 1 remainder 55 |
| 3 | 90 ÷ 55 = 1 remainder 35 |
| 4 | 55 ÷ 35 = 1 remainder 20 |
| 5 | 35 ÷ 20 = 1 remainder 15 |
| 6 | 20 ÷ 15 = 1 remainder 5 |
| 7 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 196 | 8428 |
| 186 and 41 | 7626 |
| 63 and 95 | 5985 |
| 11 and 105 | 1155 |
| 65 and 129 | 8385 |