Least Common Multiple (LCM) of 135 and 148
The least common multiple (LCM) of 135 and 148 is 19980.
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 148?
First, calculate the GCD of 135 and 148 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 148 = 0 remainder 135 |
| 2 | 148 ÷ 135 = 1 remainder 13 |
| 3 | 135 ÷ 13 = 10 remainder 5 |
| 4 | 13 ÷ 5 = 2 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 27 | 1026 |
| 105 and 164 | 17220 |
| 61 and 105 | 6405 |
| 177 and 116 | 20532 |
| 33 and 65 | 2145 |