Least Common Multiple (LCM) of 110 and 172
The least common multiple (LCM) of 110 and 172 is 9460.
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 110 and 172?
First, calculate the GCD of 110 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 172 = 0 remainder 110 |
| 2 | 172 ÷ 110 = 1 remainder 62 |
| 3 | 110 ÷ 62 = 1 remainder 48 |
| 4 | 62 ÷ 48 = 1 remainder 14 |
| 5 | 48 ÷ 14 = 3 remainder 6 |
| 6 | 14 ÷ 6 = 2 remainder 2 |
| 7 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 51 | 5457 |
| 197 and 31 | 6107 |
| 63 and 29 | 1827 |
| 187 and 111 | 20757 |
| 194 and 154 | 14938 |