Least Common Multiple (LCM) of 78 and 136
The least common multiple (LCM) of 78 and 136 is 5304.
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 136?
First, calculate the GCD of 78 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 136 = 0 remainder 78 |
| 2 | 136 ÷ 78 = 1 remainder 58 |
| 3 | 78 ÷ 58 = 1 remainder 20 |
| 4 | 58 ÷ 20 = 2 remainder 18 |
| 5 | 20 ÷ 18 = 1 remainder 2 |
| 6 | 18 ÷ 2 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 125 | 4125 |
| 143 and 59 | 8437 |
| 166 and 153 | 25398 |
| 52 and 125 | 6500 |
| 80 and 166 | 6640 |