Least Common Multiple (LCM) of 42 and 135
The least common multiple (LCM) of 42 and 135 is 1890.
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 42 and 135?
First, calculate the GCD of 42 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 135 = 0 remainder 42 |
| 2 | 135 ÷ 42 = 3 remainder 9 |
| 3 | 42 ÷ 9 = 4 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 56 | 3304 |
| 144 and 113 | 16272 |
| 113 and 30 | 3390 |
| 38 and 171 | 342 |
| 74 and 45 | 3330 |