Least Common Multiple (LCM) of 78 and 45
The least common multiple (LCM) of 78 and 45 is 1170.
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 45?
First, calculate the GCD of 78 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 45 = 1 remainder 33 |
| 2 | 45 ÷ 33 = 1 remainder 12 |
| 3 | 33 ÷ 12 = 2 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 118 | 3658 |
| 25 and 178 | 4450 |
| 108 and 168 | 1512 |
| 145 and 83 | 12035 |
| 106 and 165 | 17490 |