Least Common Multiple (LCM) of 115 and 90
The least common multiple (LCM) of 115 and 90 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 115 and 90?
First, calculate the GCD of 115 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 90 = 1 remainder 25 |
| 2 | 90 ÷ 25 = 3 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 |
|---|---|
| 193 and 37 | 7141 |
| 120 and 182 | 10920 |
| 34 and 156 | 2652 |
| 69 and 80 | 5520 |
| 98 and 48 | 2352 |