Least Common Multiple (LCM) of 188 and 78
The least common multiple (LCM) of 188 and 78 is 7332.
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 188 and 78?
First, calculate the GCD of 188 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 78 = 2 remainder 32 |
| 2 | 78 ÷ 32 = 2 remainder 14 |
| 3 | 32 ÷ 14 = 2 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 28 | 3948 |
| 166 and 97 | 16102 |
| 169 and 51 | 8619 |
| 149 and 193 | 28757 |
| 200 and 100 | 200 |