Least Common Multiple (LCM) of 172 and 111
The least common multiple (LCM) of 172 and 111 is 19092.
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 111?
First, calculate the GCD of 172 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 111 = 1 remainder 61 |
| 2 | 111 ÷ 61 = 1 remainder 50 |
| 3 | 61 ÷ 50 = 1 remainder 11 |
| 4 | 50 ÷ 11 = 4 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 81 | 2349 |
| 113 and 81 | 9153 |
| 63 and 189 | 189 |
| 22 and 57 | 1254 |
| 54 and 20 | 540 |