Least Common Multiple (LCM) of 107 and 172
The least common multiple (LCM) of 107 and 172 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 107 and 172?
First, calculate the GCD of 107 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 172 = 0 remainder 107 |
| 2 | 172 ÷ 107 = 1 remainder 65 |
| 3 | 107 ÷ 65 = 1 remainder 42 |
| 4 | 65 ÷ 42 = 1 remainder 23 |
| 5 | 42 ÷ 23 = 1 remainder 19 |
| 6 | 23 ÷ 19 = 1 remainder 4 |
| 7 | 19 ÷ 4 = 4 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 67 | 12663 |
| 117 and 136 | 15912 |
| 90 and 170 | 1530 |
| 33 and 77 | 231 |
| 156 and 173 | 26988 |