Least Common Multiple (LCM) of 175 and 65
The least common multiple (LCM) of 175 and 65 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 175 and 65?
First, calculate the GCD of 175 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 65 = 2 remainder 45 |
| 2 | 65 ÷ 45 = 1 remainder 20 |
| 3 | 45 ÷ 20 = 2 remainder 5 |
| 4 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 66 and 141 | 3102 |
| 104 and 58 | 3016 |
| 100 and 24 | 600 |
| 70 and 108 | 3780 |
| 101 and 122 | 12322 |