Least Common Multiple (LCM) of 172 and 190
The least common multiple (LCM) of 172 and 190 is 16340.
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 190?
First, calculate the GCD of 172 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 190 = 0 remainder 172 |
| 2 | 190 ÷ 172 = 1 remainder 18 |
| 3 | 172 ÷ 18 = 9 remainder 10 |
| 4 | 18 ÷ 10 = 1 remainder 8 |
| 5 | 10 ÷ 8 = 1 remainder 2 |
| 6 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 99 | 10494 |
| 195 and 86 | 16770 |
| 131 and 41 | 5371 |
| 72 and 91 | 6552 |
| 43 and 15 | 645 |