Least Common Multiple (LCM) of 135 and 159
The least common multiple (LCM) of 135 and 159 is 7155.
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 159?
First, calculate the GCD of 135 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 159 = 0 remainder 135 |
| 2 | 159 ÷ 135 = 1 remainder 24 |
| 3 | 135 ÷ 24 = 5 remainder 15 |
| 4 | 24 ÷ 15 = 1 remainder 9 |
| 5 | 15 ÷ 9 = 1 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 42 | 4242 |
| 186 and 131 | 24366 |
| 43 and 90 | 3870 |
| 181 and 40 | 7240 |
| 41 and 101 | 4141 |