Least Common Multiple (LCM) of 54 and 78
The least common multiple (LCM) of 54 and 78 is 702.
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 54 and 78?
First, calculate the GCD of 54 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 54 ÷ 78 = 0 remainder 54 |
| 2 | 78 ÷ 54 = 1 remainder 24 |
| 3 | 54 ÷ 24 = 2 remainder 6 |
| 4 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 70 | 10990 |
| 16 and 85 | 1360 |
| 92 and 24 | 552 |
| 145 and 43 | 6235 |
| 160 and 140 | 1120 |