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 |
|---|---|
| 160 and 180 | 1440 |
| 125 and 67 | 8375 |
| 158 and 139 | 21962 |
| 100 and 158 | 7900 |
| 109 and 43 | 4687 |