Least Common Multiple (LCM) of 78 and 35
The least common multiple (LCM) of 78 and 35 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 78 and 35?
First, calculate the GCD of 78 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 35 = 2 remainder 8 |
| 2 | 35 ÷ 8 = 4 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 100 | 8100 |
| 40 and 76 | 760 |
| 160 and 87 | 13920 |
| 125 and 12 | 1500 |
| 31 and 163 | 5053 |