Least Common Multiple (LCM) of 135 and 178
The least common multiple (LCM) of 135 and 178 is 24030.
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 178?
First, calculate the GCD of 135 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 178 = 0 remainder 135 |
| 2 | 178 ÷ 135 = 1 remainder 43 |
| 3 | 135 ÷ 43 = 3 remainder 6 |
| 4 | 43 ÷ 6 = 7 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 59 | 3717 |
| 15 and 104 | 1560 |
| 80 and 171 | 13680 |
| 20 and 128 | 640 |
| 54 and 115 | 6210 |