Least Common Multiple (LCM) of 175 and 113
The least common multiple (LCM) of 175 and 113 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 175 and 113?
First, calculate the GCD of 175 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 113 = 1 remainder 62 |
| 2 | 113 ÷ 62 = 1 remainder 51 |
| 3 | 62 ÷ 51 = 1 remainder 11 |
| 4 | 51 ÷ 11 = 4 remainder 7 |
| 5 | 11 ÷ 7 = 1 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 127 | 23114 |
| 103 and 13 | 1339 |
| 105 and 110 | 2310 |
| 119 and 64 | 7616 |
| 131 and 188 | 24628 |