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 |
|---|---|
| 89 and 47 | 4183 |
| 124 and 73 | 9052 |
| 135 and 16 | 2160 |
| 48 and 155 | 7440 |
| 156 and 20 | 780 |