Least Common Multiple (LCM) of 78 and 149
The least common multiple (LCM) of 78 and 149 is 11622.
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 149?
First, calculate the GCD of 78 and 149 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 149 = 0 remainder 78 |
| 2 | 149 ÷ 78 = 1 remainder 71 |
| 3 | 78 ÷ 71 = 1 remainder 7 |
| 4 | 71 ÷ 7 = 10 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 60 | 180 |
| 187 and 80 | 14960 |
| 102 and 104 | 5304 |
| 57 and 136 | 7752 |
| 130 and 108 | 7020 |