Least Common Multiple (LCM) of 90 and 65
The least common multiple (LCM) of 90 and 65 is 1170.
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 65?
First, calculate the GCD of 90 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 65 = 1 remainder 25 |
| 2 | 65 ÷ 25 = 2 remainder 15 |
| 3 | 25 ÷ 15 = 1 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 10 | 1130 |
| 192 and 177 | 11328 |
| 32 and 73 | 2336 |
| 123 and 176 | 21648 |
| 29 and 43 | 1247 |