Least Common Multiple (LCM) of 20 and 78
The least common multiple (LCM) of 20 and 78 is 780.
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 20 and 78?
First, calculate the GCD of 20 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 20 ÷ 78 = 0 remainder 20 |
| 2 | 78 ÷ 20 = 3 remainder 18 |
| 3 | 20 ÷ 18 = 1 remainder 2 |
| 4 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 56 and 104 | 728 |
| 104 and 53 | 5512 |
| 64 and 187 | 11968 |
| 169 and 117 | 1521 |
| 29 and 172 | 4988 |