Least Common Multiple (LCM) of 135 and 78
The least common multiple (LCM) of 135 and 78 is 3510.
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 78?
First, calculate the GCD of 135 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 78 = 1 remainder 57 |
| 2 | 78 ÷ 57 = 1 remainder 21 |
| 3 | 57 ÷ 21 = 2 remainder 15 |
| 4 | 21 ÷ 15 = 1 remainder 6 |
| 5 | 15 ÷ 6 = 2 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 43 | 3139 |
| 32 and 178 | 2848 |
| 103 and 66 | 6798 |
| 150 and 31 | 4650 |
| 183 and 70 | 12810 |