Least Common Multiple (LCM) of 135 and 84
The least common multiple (LCM) of 135 and 84 is 3780.
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 84?
First, calculate the GCD of 135 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 84 = 1 remainder 51 |
| 2 | 84 ÷ 51 = 1 remainder 33 |
| 3 | 51 ÷ 33 = 1 remainder 18 |
| 4 | 33 ÷ 18 = 1 remainder 15 |
| 5 | 18 ÷ 15 = 1 remainder 3 |
| 6 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 86 | 2322 |
| 72 and 144 | 144 |
| 146 and 56 | 4088 |
| 97 and 32 | 3104 |
| 65 and 116 | 7540 |