Least Common Multiple (LCM) of 145 and 192
The least common multiple (LCM) of 145 and 192 is 27840.
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 145 and 192?
First, calculate the GCD of 145 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 192 = 0 remainder 145 |
| 2 | 192 ÷ 145 = 1 remainder 47 |
| 3 | 145 ÷ 47 = 3 remainder 4 |
| 4 | 47 ÷ 4 = 11 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 173 | 13321 |
| 56 and 120 | 840 |
| 114 and 80 | 4560 |
| 10 and 19 | 190 |
| 91 and 99 | 9009 |