Least Common Multiple (LCM) of 149 and 110
The least common multiple (LCM) of 149 and 110 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 149 and 110?
First, calculate the GCD of 149 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 110 = 1 remainder 39 |
| 2 | 110 ÷ 39 = 2 remainder 32 |
| 3 | 39 ÷ 32 = 1 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 79 | 10823 |
| 177 and 86 | 15222 |
| 84 and 196 | 588 |
| 83 and 24 | 1992 |
| 165 and 119 | 19635 |