Least Common Multiple (LCM) of 135 and 173
The least common multiple (LCM) of 135 and 173 is 23355.
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 173?
First, calculate the GCD of 135 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 173 = 0 remainder 135 |
| 2 | 173 ÷ 135 = 1 remainder 38 |
| 3 | 135 ÷ 38 = 3 remainder 21 |
| 4 | 38 ÷ 21 = 1 remainder 17 |
| 5 | 21 ÷ 17 = 1 remainder 4 |
| 6 | 17 ÷ 4 = 4 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 199 | 34825 |
| 144 and 103 | 14832 |
| 34 and 53 | 1802 |
| 16 and 194 | 1552 |
| 39 and 135 | 1755 |