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 |
|---|---|
| 48 and 194 | 4656 |
| 157 and 71 | 11147 |
| 149 and 81 | 12069 |
| 23 and 84 | 1932 |
| 14 and 171 | 2394 |