Least Common Multiple (LCM) of 78 and 133
The least common multiple (LCM) of 78 and 133 is 10374.
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 133?
First, calculate the GCD of 78 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 78 ÷ 133 = 0 remainder 78 |
| 2 | 133 ÷ 78 = 1 remainder 55 |
| 3 | 78 ÷ 55 = 1 remainder 23 |
| 4 | 55 ÷ 23 = 2 remainder 9 |
| 5 | 23 ÷ 9 = 2 remainder 5 |
| 6 | 9 ÷ 5 = 1 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 28 and 107 | 2996 |
| 131 and 90 | 11790 |
| 40 and 68 | 680 |
| 67 and 119 | 7973 |
| 115 and 17 | 1955 |