Least Common Multiple (LCM) of 135 and 156
The least common multiple (LCM) of 135 and 156 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 135 and 156?
First, calculate the GCD of 135 and 156 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 156 = 0 remainder 135 |
| 2 | 156 ÷ 135 = 1 remainder 21 |
| 3 | 135 ÷ 21 = 6 remainder 9 |
| 4 | 21 ÷ 9 = 2 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 148 | 4440 |
| 112 and 57 | 6384 |
| 140 and 200 | 1400 |
| 20 and 103 | 2060 |
| 199 and 120 | 23880 |