Least Common Multiple (LCM) of 175 and 72
The least common multiple (LCM) of 175 and 72 is 12600.
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 72?
First, calculate the GCD of 175 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 72 = 2 remainder 31 |
| 2 | 72 ÷ 31 = 2 remainder 10 |
| 3 | 31 ÷ 10 = 3 remainder 1 |
| 4 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 69 | 345 |
| 92 and 189 | 17388 |
| 110 and 144 | 7920 |
| 110 and 69 | 7590 |
| 80 and 172 | 3440 |