Least Common Multiple (LCM) of 135 and 61
The least common multiple (LCM) of 135 and 61 is 8235.
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 61?
First, calculate the GCD of 135 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 61 = 2 remainder 13 |
| 2 | 61 ÷ 13 = 4 remainder 9 |
| 3 | 13 ÷ 9 = 1 remainder 4 |
| 4 | 9 ÷ 4 = 2 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 22 and 187 | 374 |
| 72 and 183 | 4392 |
| 47 and 150 | 7050 |
| 113 and 139 | 15707 |
| 54 and 99 | 594 |