Least Common Multiple (LCM) of 120 and 135
The least common multiple (LCM) of 120 and 135 is 1080.
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 120 and 135?
First, calculate the GCD of 120 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 135 = 0 remainder 120 |
| 2 | 135 ÷ 120 = 1 remainder 15 |
| 3 | 120 ÷ 15 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 77 | 1386 |
| 159 and 35 | 5565 |
| 193 and 59 | 11387 |
| 15 and 18 | 90 |
| 138 and 118 | 8142 |