Least Common Multiple (LCM) of 135 and 149
The least common multiple (LCM) of 135 and 149 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 135 and 149?
First, calculate the GCD of 135 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 149 = 0 remainder 135 |
| 2 | 149 ÷ 135 = 1 remainder 14 |
| 3 | 135 ÷ 14 = 9 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 149 | 16539 |
| 117 and 183 | 7137 |
| 126 and 163 | 20538 |
| 13 and 73 | 949 |
| 138 and 162 | 3726 |