Least Common Multiple (LCM) of 135 and 174
The least common multiple (LCM) of 135 and 174 is 7830.
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 174?
First, calculate the GCD of 135 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 174 = 0 remainder 135 |
| 2 | 174 ÷ 135 = 1 remainder 39 |
| 3 | 135 ÷ 39 = 3 remainder 18 |
| 4 | 39 ÷ 18 = 2 remainder 3 |
| 5 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 141 | 5640 |
| 16 and 75 | 1200 |
| 128 and 65 | 8320 |
| 155 and 71 | 11005 |
| 114 and 21 | 798 |