Least Common Multiple (LCM) of 30 and 78
The least common multiple (LCM) of 30 and 78 is 390.
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 30 and 78?
First, calculate the GCD of 30 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 78 = 0 remainder 30 |
| 2 | 78 ÷ 30 = 2 remainder 18 |
| 3 | 30 ÷ 18 = 1 remainder 12 |
| 4 | 18 ÷ 12 = 1 remainder 6 |
| 5 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 102 | 2856 |
| 44 and 192 | 2112 |
| 57 and 80 | 4560 |
| 74 and 182 | 6734 |
| 165 and 90 | 990 |