Least Common Multiple (LCM) of 135 and 52
The least common multiple (LCM) of 135 and 52 is 7020.
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 52?
First, calculate the GCD of 135 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 52 = 2 remainder 31 |
| 2 | 52 ÷ 31 = 1 remainder 21 |
| 3 | 31 ÷ 21 = 1 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 127 | 17399 |
| 50 and 85 | 850 |
| 200 and 167 | 33400 |
| 71 and 49 | 3479 |
| 57 and 99 | 1881 |