Least Common Multiple (LCM) of 78 and 101
The least common multiple (LCM) of 78 and 101 is 7878.
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 101?
First, calculate the GCD of 78 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 101 = 0 remainder 78 |
| 2 | 101 ÷ 78 = 1 remainder 23 |
| 3 | 78 ÷ 23 = 3 remainder 9 |
| 4 | 23 ÷ 9 = 2 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 149 and 168 | 25032 |
| 139 and 110 | 15290 |
| 104 and 145 | 15080 |
| 189 and 34 | 6426 |
| 185 and 131 | 24235 |