Least Common Multiple (LCM) of 178 and 108
The least common multiple (LCM) of 178 and 108 is 9612.
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 108?
First, calculate the GCD of 178 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 108 = 1 remainder 70 |
| 2 | 108 ÷ 70 = 1 remainder 38 |
| 3 | 70 ÷ 38 = 1 remainder 32 |
| 4 | 38 ÷ 32 = 1 remainder 6 |
| 5 | 32 ÷ 6 = 5 remainder 2 |
| 6 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 58 and 175 | 10150 |
| 37 and 193 | 7141 |
| 166 and 158 | 13114 |
| 147 and 40 | 5880 |
| 77 and 24 | 1848 |