Least Common Multiple (LCM) of 78 and 188
The least common multiple (LCM) of 78 and 188 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 78 and 188?
First, calculate the GCD of 78 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 188 = 0 remainder 78 |
| 2 | 188 ÷ 78 = 2 remainder 32 |
| 3 | 78 ÷ 32 = 2 remainder 14 |
| 4 | 32 ÷ 14 = 2 remainder 4 |
| 5 | 14 ÷ 4 = 3 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 89 | 10947 |
| 136 and 164 | 5576 |
| 91 and 120 | 10920 |
| 161 and 78 | 12558 |
| 21 and 10 | 210 |