Least Common Multiple (LCM) of 69 and 135
The least common multiple (LCM) of 69 and 135 is 3105.
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 69 and 135?
First, calculate the GCD of 69 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 69 ÷ 135 = 0 remainder 69 |
| 2 | 135 ÷ 69 = 1 remainder 66 |
| 3 | 69 ÷ 66 = 1 remainder 3 |
| 4 | 66 ÷ 3 = 22 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 137 | 10549 |
| 108 and 90 | 540 |
| 162 and 99 | 1782 |
| 162 and 70 | 5670 |
| 163 and 15 | 2445 |