Least Common Multiple (LCM) of 149 and 115
The least common multiple (LCM) of 149 and 115 is 17135.
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 115?
First, calculate the GCD of 149 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 115 = 1 remainder 34 |
| 2 | 115 ÷ 34 = 3 remainder 13 |
| 3 | 34 ÷ 13 = 2 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 73 | 13870 |
| 49 and 121 | 5929 |
| 35 and 101 | 3535 |
| 185 and 42 | 7770 |
| 102 and 183 | 6222 |