Least Common Multiple (LCM) of 156 and 135
The least common multiple (LCM) of 156 and 135 is 7020.
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 156 and 135?
First, calculate the GCD of 156 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 156 ÷ 135 = 1 remainder 21 |
| 2 | 135 ÷ 21 = 6 remainder 9 |
| 3 | 21 ÷ 9 = 2 remainder 3 |
| 4 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 20 | 1780 |
| 105 and 30 | 210 |
| 181 and 100 | 18100 |
| 175 and 46 | 8050 |
| 179 and 110 | 19690 |