Least Common Multiple (LCM) of 145 and 172
The least common multiple (LCM) of 145 and 172 is 24940.
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 172?
First, calculate the GCD of 145 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 172 = 0 remainder 145 |
| 2 | 172 ÷ 145 = 1 remainder 27 |
| 3 | 145 ÷ 27 = 5 remainder 10 |
| 4 | 27 ÷ 10 = 2 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 89 | 15041 |
| 177 and 190 | 33630 |
| 115 and 47 | 5405 |
| 102 and 20 | 1020 |
| 85 and 45 | 765 |