Least Common Multiple (LCM) of 172 and 145
The least common multiple (LCM) of 172 and 145 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 172 and 145?
First, calculate the GCD of 172 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 145 = 1 remainder 27 |
| 2 | 145 ÷ 27 = 5 remainder 10 |
| 3 | 27 ÷ 10 = 2 remainder 7 |
| 4 | 10 ÷ 7 = 1 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 53 | 3286 |
| 200 and 180 | 1800 |
| 80 and 143 | 11440 |
| 111 and 178 | 19758 |
| 96 and 47 | 4512 |