Least Common Multiple (LCM) of 90 and 115
The least common multiple (LCM) of 90 and 115 is 2070.
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 115?
First, calculate the GCD of 90 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 90 ÷ 115 = 0 remainder 90 |
| 2 | 115 ÷ 90 = 1 remainder 25 |
| 3 | 90 ÷ 25 = 3 remainder 15 |
| 4 | 25 ÷ 15 = 1 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 15 | 510 |
| 165 and 197 | 32505 |
| 40 and 184 | 920 |
| 63 and 164 | 10332 |
| 59 and 115 | 6785 |