Least Common Multiple (LCM) of 35 and 78
The least common multiple (LCM) of 35 and 78 is 2730.
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 35 and 78?
First, calculate the GCD of 35 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 35 ÷ 78 = 0 remainder 35 |
| 2 | 78 ÷ 35 = 2 remainder 8 |
| 3 | 35 ÷ 8 = 4 remainder 3 |
| 4 | 8 ÷ 3 = 2 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 169 | 3380 |
| 123 and 64 | 7872 |
| 186 and 33 | 2046 |
| 71 and 19 | 1349 |
| 169 and 109 | 18421 |