Least Common Multiple (LCM) of 172 and 195
The least common multiple (LCM) of 172 and 195 is 33540.
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 195?
First, calculate the GCD of 172 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 195 = 0 remainder 172 |
| 2 | 195 ÷ 172 = 1 remainder 23 |
| 3 | 172 ÷ 23 = 7 remainder 11 |
| 4 | 23 ÷ 11 = 2 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 35 | 1330 |
| 181 and 90 | 16290 |
| 65 and 86 | 5590 |
| 166 and 199 | 33034 |
| 178 and 195 | 34710 |