Least Common Multiple (LCM) of 78 and 100
The least common multiple (LCM) of 78 and 100 is 3900.
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 100?
First, calculate the GCD of 78 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 100 = 0 remainder 78 |
| 2 | 100 ÷ 78 = 1 remainder 22 |
| 3 | 78 ÷ 22 = 3 remainder 12 |
| 4 | 22 ÷ 12 = 1 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 146 and 71 | 10366 |
| 72 and 152 | 1368 |
| 35 and 157 | 5495 |
| 14 and 109 | 1526 |
| 114 and 42 | 798 |