Least Common Multiple (LCM) of 135 and 70
The least common multiple (LCM) of 135 and 70 is 1890.
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 70?
First, calculate the GCD of 135 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 70 = 1 remainder 65 |
| 2 | 70 ÷ 65 = 1 remainder 5 |
| 3 | 65 ÷ 5 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 186 | 1674 |
| 114 and 159 | 6042 |
| 84 and 83 | 6972 |
| 88 and 37 | 3256 |
| 156 and 178 | 13884 |