Least Common Multiple (LCM) of 100 and 78
The least common multiple (LCM) of 100 and 78 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 100 and 78?
First, calculate the GCD of 100 and 78 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 78 = 1 remainder 22 |
| 2 | 78 ÷ 22 = 3 remainder 12 |
| 3 | 22 ÷ 12 = 1 remainder 10 |
| 4 | 12 ÷ 10 = 1 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 34 and 79 | 2686 |
| 34 and 179 | 6086 |
| 115 and 187 | 21505 |
| 165 and 113 | 18645 |
| 131 and 56 | 7336 |