Least Common Multiple (LCM) of 78 and 147
The least common multiple (LCM) of 78 and 147 is 3822.
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 147?
First, calculate the GCD of 78 and 147 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 147 = 0 remainder 78 |
| 2 | 147 ÷ 78 = 1 remainder 69 |
| 3 | 78 ÷ 69 = 1 remainder 9 |
| 4 | 69 ÷ 9 = 7 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 48 | 7536 |
| 149 and 175 | 26075 |
| 109 and 149 | 16241 |
| 199 and 163 | 32437 |
| 29 and 25 | 725 |