Least Common Multiple (LCM) of 135 and 195
The least common multiple (LCM) of 135 and 195 is 1755.
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 195?
First, calculate the GCD of 135 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 195 = 0 remainder 135 |
| 2 | 195 ÷ 135 = 1 remainder 60 |
| 3 | 135 ÷ 60 = 2 remainder 15 |
| 4 | 60 ÷ 15 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 106 | 4770 |
| 124 and 44 | 1364 |
| 160 and 96 | 480 |
| 43 and 166 | 7138 |
| 55 and 96 | 5280 |