Least Common Multiple (LCM) of 65 and 175
The least common multiple (LCM) of 65 and 175 is 2275.
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 175?
First, calculate the GCD of 65 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 175 = 0 remainder 65 |
| 2 | 175 ÷ 65 = 2 remainder 45 |
| 3 | 65 ÷ 45 = 1 remainder 20 |
| 4 | 45 ÷ 20 = 2 remainder 5 |
| 5 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 83 | 14525 |
| 48 and 78 | 624 |
| 20 and 17 | 340 |
| 26 and 32 | 416 |
| 115 and 112 | 12880 |