Least Common Multiple (LCM) of 115 and 150
The least common multiple (LCM) of 115 and 150 is 3450.
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 150?
First, calculate the GCD of 115 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 150 = 0 remainder 115 |
| 2 | 150 ÷ 115 = 1 remainder 35 |
| 3 | 115 ÷ 35 = 3 remainder 10 |
| 4 | 35 ÷ 10 = 3 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 142 | 11786 |
| 173 and 91 | 15743 |
| 12 and 133 | 1596 |
| 165 and 93 | 5115 |
| 116 and 194 | 11252 |