Least Common Multiple (LCM) of 78 and 168
The least common multiple (LCM) of 78 and 168 is 2184.
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 168?
First, calculate the GCD of 78 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 168 = 0 remainder 78 |
| 2 | 168 ÷ 78 = 2 remainder 12 |
| 3 | 78 ÷ 12 = 6 remainder 6 |
| 4 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 32 | 1248 |
| 129 and 59 | 7611 |
| 126 and 115 | 14490 |
| 74 and 20 | 740 |
| 83 and 119 | 9877 |