Least Common Multiple (LCM) of 95 and 135
The least common multiple (LCM) of 95 and 135 is 2565.
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 95 and 135?
First, calculate the GCD of 95 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 95 ÷ 135 = 0 remainder 95 |
| 2 | 135 ÷ 95 = 1 remainder 40 |
| 3 | 95 ÷ 40 = 2 remainder 15 |
| 4 | 40 ÷ 15 = 2 remainder 10 |
| 5 | 15 ÷ 10 = 1 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 67 | 5025 |
| 147 and 82 | 12054 |
| 115 and 97 | 11155 |
| 165 and 12 | 660 |
| 112 and 21 | 336 |