Least Common Multiple (LCM) of 65 and 95
The least common multiple (LCM) of 65 and 95 is 1235.
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 65 and 95?
First, calculate the GCD of 65 and 95 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 95 = 0 remainder 65 |
| 2 | 95 ÷ 65 = 1 remainder 30 |
| 3 | 65 ÷ 30 = 2 remainder 5 |
| 4 | 30 ÷ 5 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 19 | 2508 |
| 180 and 65 | 2340 |
| 175 and 113 | 19775 |
| 54 and 58 | 1566 |
| 168 and 169 | 28392 |