Least Common Multiple (LCM) of 135 and 42
The least common multiple (LCM) of 135 and 42 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 135 and 42?
First, calculate the GCD of 135 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 42 = 3 remainder 9 |
| 2 | 42 ÷ 9 = 4 remainder 6 |
| 3 | 9 ÷ 6 = 1 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 71 | 10295 |
| 135 and 123 | 5535 |
| 76 and 80 | 1520 |
| 31 and 40 | 1240 |
| 125 and 62 | 7750 |