Least Common Multiple (LCM) of 110 and 149
The least common multiple (LCM) of 110 and 149 is 16390.
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 149?
First, calculate the GCD of 110 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 149 = 0 remainder 110 |
| 2 | 149 ÷ 110 = 1 remainder 39 |
| 3 | 110 ÷ 39 = 2 remainder 32 |
| 4 | 39 ÷ 32 = 1 remainder 7 |
| 5 | 32 ÷ 7 = 4 remainder 4 |
| 6 | 7 ÷ 4 = 1 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 80 | 720 |
| 157 and 57 | 8949 |
| 180 and 60 | 180 |
| 186 and 12 | 372 |
| 140 and 159 | 22260 |