Least Common Multiple (LCM) of 178 and 135
The least common multiple (LCM) of 178 and 135 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 178 and 135?
First, calculate the GCD of 178 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 135 = 1 remainder 43 |
| 2 | 135 ÷ 43 = 3 remainder 6 |
| 3 | 43 ÷ 6 = 7 remainder 1 |
| 4 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 100 and 137 | 13700 |
| 100 and 84 | 2100 |
| 15 and 40 | 120 |
| 78 and 156 | 156 |
| 169 and 59 | 9971 |