Least Common Multiple (LCM) of 172 and 107
The least common multiple (LCM) of 172 and 107 is 18404.
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 172 and 107?
First, calculate the GCD of 172 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 107 = 1 remainder 65 |
| 2 | 107 ÷ 65 = 1 remainder 42 |
| 3 | 65 ÷ 42 = 1 remainder 23 |
| 4 | 42 ÷ 23 = 1 remainder 19 |
| 5 | 23 ÷ 19 = 1 remainder 4 |
| 6 | 19 ÷ 4 = 4 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 192 | 960 |
| 133 and 118 | 15694 |
| 82 and 129 | 10578 |
| 97 and 184 | 17848 |
| 134 and 58 | 3886 |