Least Common Multiple (LCM) of 113 and 175
The least common multiple (LCM) of 113 and 175 is 19775.
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 113 and 175?
First, calculate the GCD of 113 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 175 = 0 remainder 113 |
| 2 | 175 ÷ 113 = 1 remainder 62 |
| 3 | 113 ÷ 62 = 1 remainder 51 |
| 4 | 62 ÷ 51 = 1 remainder 11 |
| 5 | 51 ÷ 11 = 4 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 49 | 6272 |
| 194 and 139 | 26966 |
| 24 and 121 | 2904 |
| 12 and 24 | 24 |
| 195 and 200 | 7800 |