Least Common Multiple (LCM) of 80 and 175
The least common multiple (LCM) of 80 and 175 is 2800.
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 80 and 175?
First, calculate the GCD of 80 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 175 = 0 remainder 80 |
| 2 | 175 ÷ 80 = 2 remainder 15 |
| 3 | 80 ÷ 15 = 5 remainder 5 |
| 4 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 96 | 288 |
| 127 and 152 | 19304 |
| 135 and 57 | 2565 |
| 114 and 89 | 10146 |
| 115 and 117 | 13455 |