Least Common Multiple (LCM) of 149 and 135
The least common multiple (LCM) of 149 and 135 is 20115.
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 135?
First, calculate the GCD of 149 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 149 ÷ 135 = 1 remainder 14 |
| 2 | 135 ÷ 14 = 9 remainder 9 |
| 3 | 14 ÷ 9 = 1 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 45 | 315 |
| 86 and 142 | 6106 |
| 12 and 92 | 276 |
| 87 and 96 | 2784 |
| 141 and 82 | 11562 |