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 |
|---|---|
| 25 and 56 | 1400 |
| 197 and 107 | 21079 |
| 103 and 105 | 10815 |
| 183 and 26 | 4758 |
| 69 and 145 | 10005 |