Least Common Multiple (LCM) of 135 and 142
The least common multiple (LCM) of 135 and 142 is 19170.
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 142?
First, calculate the GCD of 135 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 142 = 0 remainder 135 |
| 2 | 142 ÷ 135 = 1 remainder 7 |
| 3 | 135 ÷ 7 = 19 remainder 2 |
| 4 | 7 ÷ 2 = 3 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 28 | 84 |
| 99 and 152 | 15048 |
| 133 and 196 | 3724 |
| 78 and 10 | 390 |
| 170 and 103 | 17510 |