Least Common Multiple (LCM) of 44 and 78
The least common multiple (LCM) of 44 and 78 is 1716.
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 44 and 78?
First, calculate the GCD of 44 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 44 ÷ 78 = 0 remainder 44 |
| 2 | 78 ÷ 44 = 1 remainder 34 |
| 3 | 44 ÷ 34 = 1 remainder 10 |
| 4 | 34 ÷ 10 = 3 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 24 | 312 |
| 96 and 101 | 9696 |
| 143 and 24 | 3432 |
| 11 and 153 | 1683 |
| 17 and 99 | 1683 |