Least Common Multiple (LCM) of 78 and 42
The least common multiple (LCM) of 78 and 42 is 546.
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 42?
First, calculate the GCD of 78 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 42 = 1 remainder 36 |
| 2 | 42 ÷ 36 = 1 remainder 6 |
| 3 | 36 ÷ 6 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 28 | 2324 |
| 180 and 162 | 1620 |
| 74 and 169 | 12506 |
| 135 and 33 | 1485 |
| 123 and 193 | 23739 |