Least Common Multiple (LCM) of 175 and 107
The least common multiple (LCM) of 175 and 107 is 18725.
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 107?
First, calculate the GCD of 175 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 175 ÷ 107 = 1 remainder 68 |
| 2 | 107 ÷ 68 = 1 remainder 39 |
| 3 | 68 ÷ 39 = 1 remainder 29 |
| 4 | 39 ÷ 29 = 1 remainder 10 |
| 5 | 29 ÷ 10 = 2 remainder 9 |
| 6 | 10 ÷ 9 = 1 remainder 1 |
| 7 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 33 | 1617 |
| 128 and 109 | 13952 |
| 133 and 51 | 6783 |
| 171 and 32 | 5472 |
| 159 and 68 | 10812 |