Least Common Multiple (LCM) of 107 and 175
The least common multiple (LCM) of 107 and 175 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 107 and 175?
First, calculate the GCD of 107 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 175 = 0 remainder 107 |
| 2 | 175 ÷ 107 = 1 remainder 68 |
| 3 | 107 ÷ 68 = 1 remainder 39 |
| 4 | 68 ÷ 39 = 1 remainder 29 |
| 5 | 39 ÷ 29 = 1 remainder 10 |
| 6 | 29 ÷ 10 = 2 remainder 9 |
| 7 | 10 ÷ 9 = 1 remainder 1 |
| 8 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 184 | 10856 |
| 64 and 78 | 2496 |
| 167 and 192 | 32064 |
| 87 and 88 | 7656 |
| 133 and 105 | 1995 |