Least Common Multiple (LCM) of 172 and 165
The least common multiple (LCM) of 172 and 165 is 28380.
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 165?
First, calculate the GCD of 172 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 165 = 1 remainder 7 |
| 2 | 165 ÷ 7 = 23 remainder 4 |
| 3 | 7 ÷ 4 = 1 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 11 | 1463 |
| 136 and 199 | 27064 |
| 45 and 123 | 1845 |
| 17 and 155 | 2635 |
| 131 and 93 | 12183 |