Least Common Multiple (LCM) of 135 and 53
The least common multiple (LCM) of 135 and 53 is 7155.
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 53?
First, calculate the GCD of 135 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 53 = 2 remainder 29 |
| 2 | 53 ÷ 29 = 1 remainder 24 |
| 3 | 29 ÷ 24 = 1 remainder 5 |
| 4 | 24 ÷ 5 = 4 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 60 | 1380 |
| 81 and 141 | 3807 |
| 193 and 41 | 7913 |
| 76 and 34 | 1292 |
| 178 and 58 | 5162 |