Least Common Multiple (LCM) of 135 and 88
The least common multiple (LCM) of 135 and 88 is 11880.
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 88?
First, calculate the GCD of 135 and 88 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 88 = 1 remainder 47 |
| 2 | 88 ÷ 47 = 1 remainder 41 |
| 3 | 47 ÷ 41 = 1 remainder 6 |
| 4 | 41 ÷ 6 = 6 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 157 | 10676 |
| 155 and 178 | 27590 |
| 84 and 198 | 2772 |
| 33 and 106 | 3498 |
| 48 and 159 | 2544 |