Least Common Multiple (LCM) of 84 and 135
The least common multiple (LCM) of 84 and 135 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 84 and 135?
First, calculate the GCD of 84 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 135 = 0 remainder 84 |
| 2 | 135 ÷ 84 = 1 remainder 51 |
| 3 | 84 ÷ 51 = 1 remainder 33 |
| 4 | 51 ÷ 33 = 1 remainder 18 |
| 5 | 33 ÷ 18 = 1 remainder 15 |
| 6 | 18 ÷ 15 = 1 remainder 3 |
| 7 | 15 ÷ 3 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 86 | 5246 |
| 141 and 155 | 21855 |
| 159 and 196 | 31164 |
| 31 and 167 | 5177 |
| 111 and 34 | 3774 |