Least Common Multiple (LCM) of 78 and 152
The least common multiple (LCM) of 78 and 152 is 5928.
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 152?
First, calculate the GCD of 78 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 152 = 0 remainder 78 |
| 2 | 152 ÷ 78 = 1 remainder 74 |
| 3 | 78 ÷ 74 = 1 remainder 4 |
| 4 | 74 ÷ 4 = 18 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 89 | 1780 |
| 17 and 30 | 510 |
| 146 and 105 | 15330 |
| 149 and 29 | 4321 |
| 190 and 70 | 1330 |