Least Common Multiple (LCM) of 110 and 134
The least common multiple (LCM) of 110 and 134 is 7370.
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 134?
First, calculate the GCD of 110 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 134 = 0 remainder 110 |
| 2 | 134 ÷ 110 = 1 remainder 24 |
| 3 | 110 ÷ 24 = 4 remainder 14 |
| 4 | 24 ÷ 14 = 1 remainder 10 |
| 5 | 14 ÷ 10 = 1 remainder 4 |
| 6 | 10 ÷ 4 = 2 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 176 | 6864 |
| 67 and 172 | 11524 |
| 122 and 42 | 2562 |
| 124 and 49 | 6076 |
| 188 and 114 | 10716 |