Least Common Multiple (LCM) of 172 and 110
The least common multiple (LCM) of 172 and 110 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 172 and 110?
First, calculate the GCD of 172 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 110 = 1 remainder 62 |
| 2 | 110 ÷ 62 = 1 remainder 48 |
| 3 | 62 ÷ 48 = 1 remainder 14 |
| 4 | 48 ÷ 14 = 3 remainder 6 |
| 5 | 14 ÷ 6 = 2 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 147 | 9408 |
| 129 and 30 | 1290 |
| 67 and 163 | 10921 |
| 181 and 160 | 28960 |
| 55 and 124 | 6820 |