Least Common Multiple (LCM) of 168 and 78
The least common multiple (LCM) of 168 and 78 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 168 and 78?
First, calculate the GCD of 168 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 78 = 2 remainder 12 |
| 2 | 78 ÷ 12 = 6 remainder 6 |
| 3 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 91 and 31 | 2821 |
| 138 and 149 | 20562 |
| 128 and 99 | 12672 |
| 73 and 51 | 3723 |
| 150 and 15 | 150 |