Least Common Multiple (LCM) of 32 and 78
The least common multiple (LCM) of 32 and 78 is 1248.
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 32 and 78?
First, calculate the GCD of 32 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 78 = 0 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 |
|---|---|
| 184 and 142 | 13064 |
| 10 and 80 | 80 |
| 157 and 188 | 29516 |
| 60 and 140 | 420 |
| 106 and 163 | 17278 |