Least Common Multiple (LCM) of 45 and 78
The least common multiple (LCM) of 45 and 78 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 45 and 78?
First, calculate the GCD of 45 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 78 = 0 remainder 45 |
| 2 | 78 ÷ 45 = 1 remainder 33 |
| 3 | 45 ÷ 33 = 1 remainder 12 |
| 4 | 33 ÷ 12 = 2 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 29 | 3132 |
| 61 and 94 | 5734 |
| 174 and 63 | 3654 |
| 97 and 186 | 18042 |
| 103 and 75 | 7725 |