Least Common Multiple (LCM) of 110 and 174
The least common multiple (LCM) of 110 and 174 is 9570.
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 174?
First, calculate the GCD of 110 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 174 = 0 remainder 110 |
| 2 | 174 ÷ 110 = 1 remainder 64 |
| 3 | 110 ÷ 64 = 1 remainder 46 |
| 4 | 64 ÷ 46 = 1 remainder 18 |
| 5 | 46 ÷ 18 = 2 remainder 10 |
| 6 | 18 ÷ 10 = 1 remainder 8 |
| 7 | 10 ÷ 8 = 1 remainder 2 |
| 8 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 12 and 107 | 1284 |
| 54 and 14 | 378 |
| 42 and 146 | 3066 |
| 137 and 126 | 17262 |
| 180 and 77 | 13860 |