Least Common Multiple (LCM) of 110 and 126
The least common multiple (LCM) of 110 and 126 is 6930.
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 126?
First, calculate the GCD of 110 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 126 = 0 remainder 110 |
| 2 | 126 ÷ 110 = 1 remainder 16 |
| 3 | 110 ÷ 16 = 6 remainder 14 |
| 4 | 16 ÷ 14 = 1 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 161 and 193 | 31073 |
| 192 and 191 | 36672 |
| 13 and 63 | 819 |
| 159 and 102 | 5406 |
| 142 and 45 | 6390 |