Least Common Multiple (LCM) of 117 and 175
The least common multiple (LCM) of 117 and 175 is 20475.
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 117 and 175?
First, calculate the GCD of 117 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 175 = 0 remainder 117 |
| 2 | 175 ÷ 117 = 1 remainder 58 |
| 3 | 117 ÷ 58 = 2 remainder 1 |
| 4 | 58 ÷ 1 = 58 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 35 | 1505 |
| 25 and 111 | 2775 |
| 16 and 75 | 1200 |
| 193 and 178 | 34354 |
| 46 and 60 | 1380 |