Least Common Multiple (LCM) of 172 and 194
The least common multiple (LCM) of 172 and 194 is 16684.
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 194?
First, calculate the GCD of 172 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 194 = 0 remainder 172 |
| 2 | 194 ÷ 172 = 1 remainder 22 |
| 3 | 172 ÷ 22 = 7 remainder 18 |
| 4 | 22 ÷ 18 = 1 remainder 4 |
| 5 | 18 ÷ 4 = 4 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 51 | 1683 |
| 193 and 102 | 19686 |
| 161 and 150 | 24150 |
| 16 and 149 | 2384 |
| 73 and 166 | 12118 |